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Class 10 Exam  >  Class 10 Notes  >  Mathematics (Maths) Class 10  >  Previous Year Questions: Coordinate Geometry

Class 10 Maths Previous Year Questions - Coordinate Geometry

Previous Year Questions 2024

Q1: Assertion (A): The point which divides the line segment joining the points A (1, 2) and B (–1, 1) internally in the ratio 1 : 2 is Class 10 Maths Previous Year Questions - Coordinate Geometry
Reason (R): The coordinates of the point which divides the line segment joining the points A(x1, y1) and B(x2, y2) in the ratio m1 : m2 are Class 10 Maths Previous Year Questions - Coordinate Geometry    (2024)
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). 
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). 
(c) Assertion (A) is true but reason (R) is false. 
(d) Assertion (A) is false but reason (R) is true.

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (d)
Assertion says that point Class 10 Maths Previous Year Questions - Coordinate Geometry
divides the line joining the points A(1, 2) and B(–1, 1) in 1 : 2. 
∴ By section formula, Class 10 Maths Previous Year Questions - Coordinate Geometry
Class 10 Maths Previous Year Questions - Coordinate Geometry
Class 10 Maths Previous Year Questions - Coordinate Geometry


Q2: Find a relation between x and y such that the point P(x, y) is equidistant from the points A(7, 1) and B(3, 5).     (2024)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans:
Since, P(x, y) is equidistant from A(7, 1) and B(3, 5)
So, PA = PB
⇒ PA2 = PB2
⇒ (x – 7)2 + (y – 1)2 = (x – 3)2 + (y – 5)2
⇒ x2 + 49 – 14x + y2 + 1 – 2y = x2 + 9 – 6x + y2 + 25 – 10y
⇒ 6x – 14x + 50 – 34 + 10y – 2y = 0
⇒ – 8x + 8y + 16 = 0
⇒ 8x – 8y – 16 = 0
⇒ 8(x – y – 2) = 0
⇒ x – y – 2 = 0
⇒ x – y = 2


Q3: Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y) such that AB is a diameter of the circle. Find the value of y. Also, find the radius of the circle.      (2024)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: A (– 1, y); B(5, 7)
Since, AB is a diameter of circle and O is the centre of the circle.
OA = OB i.e., O divides AB in 1 : 1
So m1 : m2 = 1 : 1
So Class 10 Maths Previous Year Questions - Coordinate Geometry
Class 10 Maths Previous Year Questions - Coordinate Geometry⇒ Class 10 Maths Previous Year Questions - Coordinate Geometry
⇒ – 6y = y + 7
⇒ – 7y = 7
⇒ y = – 1
Point O = (2, 3), A = (–1, – 1)
Now,
Class 10 Maths Previous Year Questions - Coordinate Geometry
Class 10 Maths Previous Year Questions - Coordinate Geometry
So, radius of circles = 5 units


Q4: Find the ratio in which the line segment joining the points (5, 3) and (–1, 6) is divided by Y-axis.   (2024)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans:
If y-axis divides points (5, 3) and (–1, 6) then coordinate of that point will be (0, y). Let P(0, y) divides A(5, 3) and B(–1, 6) in k : 1.
m1 : m2 = k : 1
Class 10 Maths Previous Year Questions - Coordinate Geometry
⇒ 0 × (k + 1) = – k + 5
⇒ 0 = – k + 5
⇒ k = 5
So, m1 : m2 = 5 : 1

 

Previous Year Questions 2023


Q5: The distance of the point (-1, 7) from x-axis is  (2023)
(a) -1
(b) 7
(c) 6
(d) √50    [2023, 1 Mark]

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (b)
Distance from x-axis = y-coordinate of point = 7 units


Q6: Assertion (A): Point P(0, 2) is t be point of intersection of y-axis with the line 3x + 2y = 4.  (2023)
Reason (R): The distance of paint P(0, 2) from x-axis is 2 units.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true. 

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (b)
Point P(0, 2) is the point of intersection of y-axis with line 3x + 2y = 4

Class 10 Maths Previous Year Questions - Coordinate Geometry

Also, the distance of point P(0, 2) from x-axis is 2 units.


Q7: The distance of the point (-6, 8) from origin is  (2023)
(a) 6
(b) -6
(c) 8
(d) 10

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (d)
Distance of the point (-6, 8) from origin (0, 0)

Class 10 Maths Previous Year Questions - Coordinate Geometry

= 10 Units


Q8: The points (-4, 0), (4, 0) and (0, 3) are the vertices of a  (2023)
(a) right triangle
(b) isosceles triangle
(c) equilateral triangle
(d) scalene triangle 

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (b)
The points be A(-4, 0), B(4, 0) and C(0, 3).
Using distance formula

Class 10 Maths Previous Year Questions - Coordinate Geometry

Class 10 Maths Previous Year Questions - Coordinate Geometry
= 8 units

Class 10 Maths Previous Year Questions - Coordinate Geometry
 = 5 units

Class 10 Maths Previous Year Questions - Coordinate Geometry
 = 5 units
And, AB2 ≠  BC2 + CA2  [∵ BC = CA]
∴ ΔABC is an isosceles triangle.


Q9: The centre of a circle is (2a, a - 7). Find the values of 'a' if the circle passes through the point (11, -9). Radius of the circle is 5√2 cm.    (2023)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: Given centre of a circle is(2a, a - 7 )

Class 10 Maths Previous Year Questions - Coordinate Geometry

Radius of the circle is 5√2 cm.
∴ Distance between centre (2a, a - 7) and (11, - 9 ) = radius of circle.
Class 10 Maths Previous Year Questions - Coordinate Geometry


Q10: In what ratio, does x-axis divide the line segment joining the points A(3, 6) and B(-12, -3) ?  (2023)
(a) 1 : 2 
(b) 1 : 4
(c) 4 : 1
(d) 2 : 1

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (d)
Let the point on the x-axis be (x, 0) which divides the line segment joining the points A(3, 6) and B(-12, -3) in the ratio k : 1
Class 10 Maths Previous Year Questions - Coordinate Geometry

Using section formula, we have

Class 10 Maths Previous Year Questions - Coordinate Geometry

Hence, the required ratio is 2 : 1.


Q11: Case Study: Jagdish has a Field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O.   (2023)

Class 10 Maths Previous Year Questions - Coordinate Geometry

Based on the above information, answer the following questions:
(i) Taking O as origin, coordinates of P are (-200, 0) and of Q are (200, 0). PQRS being a square, what are the coordinates of R and S?
(ii) (a) What is the area of square PQRS?
OR
(b) What is the length of diagonal PR in square PQRS?
(iii) If S divides CA in the ratio K: 1, what is the value of K, where point A is (200, 800)?

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (i) We have. P = (-200, 0) and Q- = (200, 0)

The coordinates of R and S are (200, 400) and (-200, 400).
(ii) (a) The length PQ = 200 + 200 = 400 units.
Area of square PQRS = 400  x 400 = 160000 sq. units.

OR

(b) Length of diagonal PR = √2 length of side = 400√2 units.
(iii) Here,
Class 10 Maths Previous Year Questions - Coordinate Geometry
Using section formula, we have

Class 10 Maths Previous Year Questions - Coordinate Geometry


Previous Year Questions 2022


Q12: The line represented by 4x - 3y = 9 intersects the y-axis at   (2022)
(a) (0, -3)
(b) (9/4, 0)
(c) (-3, 0)
(d) (0, 9/4)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (a)
Given, the equation of line is 4x- 3y = 9.
Putting x = 0, we get 4 x 0 - 3y = 9 ⇒ y =  -3
So, the line 4x - 3y = 9 intersects the y-axis at (0, -3).


Q13: The point on x-axis equidistant from the points P(5, 0) and Q(-1, 0) is   (2022)
(a) (2, 0)
(b) (-2, 0)
(c) (3, 0)
(d) (2, 2)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (a)
Let coordinates of the point on the x-axis be R (x, 0).
Given, PR = QR
⇒ PR2 = QR2
⇒ (x - 5)2 + (0 - 0)2 = (x + 1)2 + (0 - 0)2
⇒ x2 - 10x + 25 = x2 + 2x + 1
⇒ 12x =24
⇒ x = 2
Required point is (2, 0).


Q14: The x-coordinate of a point P is twice its y-coordinate. If P is equidistant front Q(2, -5) and R(-3, 6), then the coordinates of P are   (2022)
(a) (8, 16)
(b) (10, 20)
(c) (20, 10)
(d) (16, 8)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (d)
Let coordinate of point P= t
So, .(x-coordinate of point P = 2t  ∴ Point is P (2t, t).
Given, PQ = RP ⇒ PQ2 = RP2
⇒ (2t - 2)2 + (t + 5)2 = (2t + 3)2 + (t - 6)2  [By distance formula]
⇒ 4t2 - 8t + 4 + t2 + 10t + 25 = 4t2+ 12t + 9  +  t2- 12t + 36
⇒ 2t = 16
t = 8
Coordinates of P are (16,  8).


Q15: The ratio in which the point (-4, 6) divides the line segment joining the points A(-6, 10) and B(3, -8) is   (2022)
(a) 2 : 5
(b) 7 : 2
(c) 2 : 7
(d) 5 : 2

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (c)
Let point P(-4, 6) divides the line segment AB in the ratio m1: m2.
Class 10 Maths Previous Year Questions - Coordinate Geometry

By section formula, we have
Class 10 Maths Previous Year Questions - Coordinate Geometry
Hence, required ratio is 2:7.


Q16: Case Study: Shivani is an interior decorator. To design her own living room, she designed wail shelves. The graph of intersecting wail shelves is given below:   (2022)Class 10 Maths Previous Year Questions - Coordinate Geometry

Based on the above information, answer the following questions:
(i) If O is the origin, then what are the coordinates of S?
(a) (-6, -4)
(b) (6, 4)
(c) (-6, 4)
(d) (6, -4)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (c)
Coordinates of S are (-6, 4).

(ii) The coordinates of the mid-point of the line segment joining D and H is
(a) Class 10 Maths Previous Year Questions - Coordinate Geometry
(b) (3, -1)
(c) (3, 1)
(d) Class 10 Maths Previous Year Questions - Coordinate Geometry

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (b)
Coordinates of D are (-2, -4) and coordinates of H are (8, 2).
∴ Midpoint of DH = Class 10 Maths Previous Year Questions - Coordinate Geometry

(iii) The ratio in which the x-axis divides the line-segment joining the points A and C is
(a) 2 : 3 
(b) 2 : 1
(c) 1 : 2
(d) 1 : 1 

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (d)
Coordinates of A are (-2, 4) and coordinates of C are (4, -4).
Let (x, 0) divides the line segment joining the points A and C in the ratio m1 : m2
By section formula, we have
Class 10 Maths Previous Year Questions - Coordinate Geometry

(iv) The distance between the points P and G is
(a) 16 units
(b) 3√74 units
(c) 2√74 units
(d) √74 units

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (c)
Coordinates of P are (-6, -4) and coordinates of G are (8, 6).
Class 10 Maths Previous Year Questions - Coordinate Geometry

(v) The coordinates of the vertices of rectangle IJKL are
(a) I(2, 0), J(2, 6), K(8,6), L(8, 2)
(b) I(2, -2), J(2, -6), K(8, - 6), L(8, -2)
(c) I(-2, 0), J(-2, 6), K(-8, 6), L(-8, 2)
(d) I(-2, 0), J(-2, -6), K(-8, -6), L(-8, -2)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (b)
Coordinates of vertices of rectangle IJKL are respectively I(2, -2), J(2, -6), K(8, -6),L(8, -2).


Previous Year Questions 2021

Q17: Case Study : Students of a school are standing in rows and columns in their school playground to celebrate their annual sports day. A, B, C and D are the positions of four students as shown in the figure.    (2021)

Class 10 Maths Previous Year Questions - Coordinate Geometry

Based on the above, answer the following questions:
(i) The figure formed by the four points A, B, C and D is a
(a) square
(b) parallelogram - v
(c) rhombus
(d) quadrilateral

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (d)
From figure coordinates are A(2, 5), B(5, 7), C(8, 6) and D(6, 3)
Now, Class 10 Maths Previous Year Questions - Coordinate Geometry

Class 10 Maths Previous Year Questions - Coordinate Geometry
Clearly, ABCD is a quadrilateral

(ii) If the sports teacher is sitting at the origin, then which of the four students is closest to him?
(a) A
(b) B
(c) C
(d) D

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (a)
Here, sports teacher is at O(0,0).
Now, Class 10 Maths Previous Year Questions - Coordinate Geometry

Class 10 Maths Previous Year Questions - Coordinate Geometry

∴ OA is the minimum distance
∴ A is closest to sports teacher.

(iii) The distance between A and C is
(a) √37 units
(b) √35 units
(c) 6 units
(d) 5 units

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (a)
Required distance = Class 10 Maths Previous Year Questions - Coordinate Geometry
= Class 10 Maths Previous Year Questions - Coordinate Geometry

(iv) The coordinates of the mid point of line segment AC are
(a) Class 10 Maths Previous Year Questions - Coordinate Geometry
(b) Class 10 Maths Previous Year Questions - Coordinate Geometry
(c) Class 10 Maths Previous Year Questions - Coordinate Geometry
(d) (5, 11)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (c)
 Coordinates of mid-point of AC are
Class 10 Maths Previous Year Questions - Coordinate Geometry

(v) If a point P divides the line segment A D in the ratio 1: 2, then coordinates of P are
(a) Class 10 Maths Previous Year Questions - Coordinate Geometry
(b) Class 10 Maths Previous Year Questions - Coordinate Geometry
(c) Class 10 Maths Previous Year Questions - Coordinate Geometry
(d) Class 10 Maths Previous Year Questions - Coordinate Geometry

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (b)
 Let point P(x, y) divides the line segment AD in the ration 1: 2.

Class 10 Maths Previous Year Questions - Coordinate Geometry

∴ Coordinates of P are Class 10 Maths Previous Year Questions - Coordinate Geometry


Previous Year Questions 2020

Q18: The distance between the points <m, -n) and (-m, n) is    (2020)
(a) Class 10 Maths Previous Year Questions - Coordinate Geometry
(b) m + n
(c) Class 10 Maths Previous Year Questions - Coordinate Geometry
(d) Class 10 Maths Previous Year Questions - Coordinate Geometry

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (c)
Required distance

Class 10 Maths Previous Year Questions - Coordinate Geometry


Q19: The distance between t he points (0, 0) and (a - b,  a + b) is    (2020)
(a) Class 10 Maths Previous Year Questions - Coordinate Geometry
(b) Class 10 Maths Previous Year Questions - Coordinate Geometry
(c) Class 10 Maths Previous Year Questions - Coordinate Geometry
(d) Class 10 Maths Previous Year Questions - Coordinate Geometry

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (d)
Required distance = Class 10 Maths Previous Year Questions - Coordinate Geometry
Class 10 Maths Previous Year Questions - Coordinate Geometry


Q20: AOBC is a rectangle whose three vertices are A[0, -3), O(0, 0) and B(4, 0). The length of its diagonal is ______.    (2020)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: In rectangle AOBC. AB is a diagonal.
Class 10 Maths Previous Year Questions - Coordinate Geometry

So,
Class 10 Maths Previous Year Questions - Coordinate GeometryClass 10 Maths Previous Year Questions - Coordinate Geometry
= 5 Units


Q21: Show that the points (7, 10), (-2, 5) and (3, -4) are vertices of an isosceles right triangle.     (2020)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: Let the given points be A(7, 10), B(-2, 5) and C(3, - 4].
Using distance Formula, we have 
Class 10 Maths Previous Year Questions - Coordinate Geometry

Since. AB = BC ∴ ABC is an isosceles triangle.
Also, AB2 + BC2 = 106 + 106 = 212 = AC2
So. ABC is an isosceles right angled triangle with ∠B = 90°.


Q22: The point on the x-axis which is equidistant from (-4, 0) and (10, 0) is    (2020)
(a) (7, 0)
(b) (5, 0)
(c) (0, 0)
(d) (3, 0)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (d)
Let coordinates of the point on the x-axis be P(x, 0). Let the given points be A(-4, 0) and B(10, 0). which also lie on x-axis.
Since P is equidistant from A and B.
∴ x = -4 + 10 / 2 = 6 / 2 = 3
So, P(3, 0) is equidistant from A(-4, 0) and B(10, 0).


Q23: If the point P(k, 0) divides the line segment joining the points A(2, -2) and B(-7, 4) in the ratio 1:2 then the value of k is    (2020)
(a) 1
(b) 2
(c) -2
(d) -1 

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (d)
Since, the point P(k 0) divides the line segment joining A(2, -2) and B(-7, 4) in the ratio 1 : 2.

Class 10 Maths Previous Year Questions - Coordinate Geometry


Q24: The centre of a circle whose end points of a diameter are (-6, 3) and (6, 4) is    (2020)
(a) (8, -1)
(b) (4, 7)
(c) Class 10 Maths Previous Year Questions - Coordinate Geometry
(d) Class 10 Maths Previous Year Questions - Coordinate Geometry    

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: (c)
Let the coordinates of centre of the circle be (x, y) and AB be the given diameter.
By Using mid-point formula.
Class 10 Maths Previous Year Questions - Coordinate Geometry

We have,

Class 10 Maths Previous Year Questions - Coordinate Geometry
∴ Coordinates of C are Class 10 Maths Previous Year Questions - Coordinate Geometry


Q25: Find the ratio in which the y-axis divides the line segment joining the points (6, -4) and (-2, -7). Also, find the point of intersection.       (2020)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: Let the point P(0, y) on y-axis divides the line segment joining the points A(6, -4) and B(-2, -7) in the ratio k : 1.
Class 10 Maths Previous Year Questions - Coordinate Geometry

By section formula, we have 
Class 10 Maths Previous Year Questions - Coordinate Geometry
Class 10 Maths Previous Year Questions - Coordinate Geometry

Hence, the required point is Class 10 Maths Previous Year Questions - Coordinate Geometry and required ratio is 3 : 1.


Q26: If the point C(-1, 2) divides internally the line segment joining A(2, 5) and B(x, y) in the ratio 3 : 4, find the coordinates of B.    (2020)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: We have, A(2, 5), B(x, y) and C(-1, 2) and point C divides AB in the ratio 3 :4.
Class 10 Maths Previous Year Questions - Coordinate Geometry
∴ Coordinates of B =  (-5, -2)


Previous Year Questions 2019


Q27: Find the value(s) of x, if the distance between the points 4(0, 0) a nd B(x, - 4) is 5 units.     (2019)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans:  Given AB = 5 units
Class 10 Maths Previous Year Questions - Coordinate Geometry


Q28: Find the point on y-axis which is equidistant from the points (5,-2) and (-3, 2).      (Delhi 2019)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: Let P(0, y) be the point on the y-axis which is equidistant from A(5, - 2) and B(-3, 2).

AP = BP ⇒ (AP)2 = (BP)2
⇒ (5 - 0)2 + (-2 - y)2 = (-3 - 0)2 + (2 - y)2
⇒ 25 + 4 + y2 + 4y = 9 + 4 + y2 - 4y
⇒ 8y = 9 - 25
⇒ y = -16/2 = -2
Hence, A and B are equidistant from (0, -2).


Q29: Find the coordinates of a point A where AB is a diameter of the circle with centre (-2, 2) and B is the point with coordinates (3, 4).    (2019)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: Let coordinates of the point A be (x, y) and O is the mid point of AB.
Class 10 Maths Previous Year Questions - Coordinate Geometry
By using mid-point formula,
we haveClass 10 Maths Previous Year Questions - Coordinate Geometry
⇒ -4 = x + 3 and4 = y + 4
⇒ x = -7 and y = 0
∴ Coordinates of A are (-7, 0).


Q30: In what ratio is the line segment joining the points P(3, -6) and Q(5, 3) divided by x-axis?     (2019)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: Let the point R(x, 0) on x-axis divides the line segment PQ in the ratio k: 1.
Class 10 Maths Previous Year Questions - Coordinate Geometry
∴ By section formula, we have
Class 10 Maths Previous Year Questions - Coordinate Geometry
∴ Required ratio is 2 : 1 .


Q31: Find the ratio in which the segment joining the points (1, -3) sod (4, 5) is divided by x-axis? Also find the coordinates of this point on x-axis.   (2019)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: Let the point P(x, 0) divides the segment joining the points A(1, -3) and B (4, 5) in the ratio k : 1
Class 10 Maths Previous Year Questions - Coordinate Geometry

Coordinates of P are Class 10 Maths Previous Year Questions - Coordinate Geometry [By Section Formula]
Since, y-coordinate of P is 0
.Class 10 Maths Previous Year Questions - Coordinate Geometry
Hence, the point P divides the line segment in the ratio 3 : 5.
Also, x-coordinate of P
= Class 10 Maths Previous Year Questions - Coordinate Geometry
∴ Coordinates of point P are (17/8, 0)


Q32: The point R divides the line segment AB, where A (- 4, 0) and B(0, 6) such that AR = 3/4 AB.
Find the coordinates of R.    (2019)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: Given,
Class 10 Maths Previous Year Questions - Coordinate Geometry
Class 10 Maths Previous Year Questions - Coordinate Geometry
∴ Coordinates of R are
Class 10 Maths Previous Year Questions - Coordinate Geometry


Q33: Find the coordinates of a point A. where AB is a diameter of the circle with centre (3, -1) and the point B is (2, 6).   [2019, 2 Marks]

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: Let the coordinates of A be (x, y). Here, 0(3, - 1] is the mid point of AB.
Class 10 Maths Previous Year Questions - Coordinate Geometry
By using mid point formula, we haveClass 10 Maths Previous Year Questions - Coordinate Geometry⇒ x = 4, y = - 8∴ Coordinates of A are (4, - 8).


Q34: The line segment joining the points A(2, 1) and B(5, -8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the fine given by 2x - y + k = 0, find the value of k.   (2019)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: Class 10 Maths Previous Year Questions - Coordinate Geometry
Let P(x1, y1) and Q(x2, y2) are the points of trisection of line segment AB.
∴ AP = PQ = QB
Now. point P divides AB internally in the ratio 1 : 2
∴ By section formula, we have  
Class 10 Maths Previous Year Questions - Coordinate Geometry
Since, point P(3, -2) lies on the line 2x - y + k = 0
⇒ 6 + 2 + k = 0
⇒ k = - 8


Q35: Find the ratio in which the line x - 3y = 0 divides the line segment joining the points (-2, -5) and (6, 3). Find the coordinates of the point of intersection.   (2019)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: Let point P(x1, y1) divides the line segment joining the points A(-2, -5) and B(6, 3) in the ratio k: 1
Class 10 Maths Previous Year Questions - Coordinate Geometry
∴ Coordinates of P are
Class 10 Maths Previous Year Questions - Coordinate Geometry
The point P lies on line x - 3y = 0
Class 10 Maths Previous Year Questions - Coordinate Geometry
∴ Required ratio is 13 : 3.Now, coordinates of P are
Class 10 Maths Previous Year Questions - Coordinate Geometry


Q36: In what ratio does the point P(-4, y) divide the line segment joining the points A(-6, 10) and B(3, -8) Hence find the value of y.   (2019)

Class 10 Maths Previous Year Questions - Coordinate Geometry  View Answer

Ans: Let the point P(-4, y) divides the line segment joining the points A and B in the ration k: 1
Class 10 Maths Previous Year Questions - Coordinate Geometry
∴ By section formula, coordinates of P are
Class 10 Maths Previous Year Questions - Coordinate Geometry
∴ Required ration is 2: 7.

Now,
Class 10 Maths Previous Year Questions - Coordinate Geometry

The document Class 10 Maths Previous Year Questions - Coordinate Geometry is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Class 10 Maths Previous Year Questions - Coordinate Geometry

1. What are the key concepts of Coordinate Geometry for Class 10?
Ans.The key concepts of Coordinate Geometry for Class 10 include the Cartesian coordinate system, distance formula, section formula, mid-point formula, and the concept of slopes of lines. Understanding how to plot points, find distances between them, and determine the coordinates of points that divide a segment in a given ratio is crucial.
2. How do you find the distance between two points in Coordinate Geometry?
Ans.To find the distance between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), you can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] This formula derives from the Pythagorean theorem and is essential for solving various problems in Coordinate Geometry.
3. What is the section formula in Coordinate Geometry?
Ans.The section formula is used to find the coordinates of a point that divides a line segment into a given ratio. If a point \( P(x, y) \) divides the line segment joining points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \), then the coordinates of point \( P \) are given by: \[ P\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right) \]
4. How can you determine the slope of a line in Coordinate Geometry?
Ans.The slope of a line passing through two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) can be calculated using the formula: \[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \] The slope indicates the steepness of the line and is a fundamental concept in understanding linear equations.
5. Can you explain the mid-point formula in Coordinate Geometry?
Ans.The mid-point formula is used to find the midpoint of a line segment between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \). The coordinates of the midpoint \( M \) are given by: \[ M\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \] This formula is useful in various applications, including finding the center of a line segment in geometric problems.
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Document Description: Previous Year Questions: Coordinate Geometry for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The notes and questions for Previous Year Questions: Coordinate Geometry have been prepared according to the Class 10 exam syllabus. Information about Previous Year Questions: Coordinate Geometry covers topics like Previous Year Questions 2024, Previous Year Questions 2023, Previous Year Questions 2022, Previous Year Questions 2021, Previous Year Questions 2020, Previous Year Questions 2019 and Previous Year Questions: Coordinate Geometry Example, for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Previous Year Questions: Coordinate Geometry.
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