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Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry    (2024)

Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

Ans: (d)


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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
Class 8 Maths Chapter 7 Previous Year Questions - Coordinate GeometryClass 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
⇒ – 6y = y + 7
⇒ – 7y = 7
⇒ y = – 1
Point O = (2, 3), A = (–1, – 1)
Now,
Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

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

Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
= 8 units

Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
 = 5 units

Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
 = 5 units
And, AB2 ≠  BC2 + CA          [∵ 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

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

Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

Using section formula, we have

Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
Using section formula, we have

Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 
⇒ x- 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 8 Maths Chapter 7 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]
⇒ 4t- 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

By section formula, we have
Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

(b) (3, -1)
(c) (3, 1)
(d) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

Ans: (c)
Coordinates of P are (-6, -4) and coordinates of G are (8, 6).
Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

Class 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

Ans: (a)
Here, sports teacher is at O(0,0).
Now, Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

Class 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

Ans: (a)
Required distance = Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
= Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

(iv) The coordinates of the mid point of line segment AC are
(a) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
(b) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
(c) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
(d) (5, 11)

Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

Ans: (c)
 Coordinates of mid-point of AC are
Class 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
(b) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
(c) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
(d) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

Class 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

∴ Coordinates of P are Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry


Previous Year Questions 2020

Q18: The distance between the points <m, -n) and (-m, n) is    (2020)
(a) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

(b) m + n
(c) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
(d) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

Ans: (c)
Required distance

Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry


Q19: The distance between t he points (0, 0) and (a - b,  a + b) is    (2020)
(a) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

(b) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
(c) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
(d) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

Ans: (d)
Required distance = Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
Class 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

Ans: In rectangle AOBC. AB is a diagonal.
Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

So,
Class 8 Maths Chapter 7 Previous Year Questions - Coordinate GeometryClass 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

(d) Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry    

Class 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

We have,

Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
∴ Coordinates of C are Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

By section formula, we have 
Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

Hence, the required point is Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

Ans:  Given AB = 5 units
Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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)= (BP)2
⇒ (5 - 0)2 + (-2 - y)2 = (-3 - 0)+ (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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
By using mid-point formula,
we haveClass 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
∴ By section formula, we have
Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

Coordinates of P are Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry [By Section Formula]
Since, y-coordinate of P is 0
.Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
Hence, the point P divides the line segment in the ratio 3 : 5.
Also, x-coordinate of P
= Class 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

Ans: Given,
Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
∴ Coordinates of R are
Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
By using mid point formula, we haveClass 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry  View Answer

Ans:  Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
∴ Coordinates of P are
Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
The point P lies on line x - 3y = 0
Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
∴ Required ratio is 13 : 3.Now, coordinates of P are
Class 8 Maths Chapter 7 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 8 Maths Chapter 7 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 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
∴ By section formula, coordinates of P are
Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry
∴ Required ration is 2: 7.

Now,
Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

The document Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

1. What is the equation of a line passing through two given points in coordinate geometry?
Ans. To find the equation of a line passing through two given points (x1, y1) and (x2, y2), we can use the formula y - y1 = m(x - x1), where m is the slope of the line given by (y2 - y1)/(x2 - x1).
2. How do you determine if two lines are parallel or perpendicular in coordinate geometry?
Ans. Two lines are parallel if their slopes are equal, i.e., m1 = m2. Two lines are perpendicular if the product of their slopes is -1, i.e., m1 * m2 = -1.
3. How can you find the distance between a point and a line in coordinate geometry?
Ans. To find the distance between a point (x1, y1) and a line Ax + By + C = 0, you can use the formula |Ax1 + By1 + C| / sqrt(A^2 + B^2).
4. What is the midpoint formula in coordinate geometry?
Ans. The midpoint formula in coordinate geometry is given by ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of the two endpoints.
5. How do you determine if a point lies on a line in coordinate geometry?
Ans. To check if a point (x1, y1) lies on a line Ax + By + C = 0, substitute x1 and y1 into the equation. If the equation holds true, the point lies on the line.
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