Previous Year Questions: Coordinate Geometry

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

 Table of contents Previous Year Questions 2024 Previous Year Questions 2023 Previous Year Questions 2022 Previous Year Questions 2021 Previous Year Questions 2020 Previous Year Questions 2019

## 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
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     (2024)

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)

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)

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

⇒ – 6y = y + 7
⇒ – 7y = 7
⇒ y = – 1
Point O = (2, 3), A = (–1, – 1)
Now,

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)

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

⇒ 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]

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.

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

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

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

= 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

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

= 8 units

= 5 units

= 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)

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

Radius of the circle is 5√2 cm.
∴ Distance between centre (2a, a - 7) and (11, - 9 ) = radius of circle.

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

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

Using section formula, we have

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)

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)?

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,

Using section formula, we have

## 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)

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)

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)

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

Ans: (c)
Let point P(-4, 6) divides the line segment AB in the ratio m1: m2.

By section formula, we have

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)

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)

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)

(b) (3, -1)
(c) (3, 1)
(d)

Ans: (b)
Coordinates of D are (-2, -4) and coordinates of H are (8, 2).
∴ Midpoint of DH =

(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

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

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

Ans: (c)
Coordinates of P are (-6, -4) and coordinates of G are (8, 6).

(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)

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)

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

Ans: (d)
From figure coordinates are A(2, 5), B(5, 7), C(8, 6) and D(6, 3)
Now,

(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

Ans: (a)
Here, sports teacher is at O(0,0).
Now,

∴ 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

Ans: (a)
Required distance =
=

(iv) The coordinates of the mid point of line segment AC are
(a)
(b)
(c)
(d) (5, 11)

Ans: (c)
Coordinates of mid-point of AC are

(v) If a point P divides the line segment A D in the ratio 1: 2, then coordinates of P are
(a)
(b)
(c)
(d)

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

∴ Coordinates of P are

## Previous Year Questions 2020

Q18: The distance between the points <m, -n) and (-m, n) is    (2020)
(a)

(b) m + n
(c)
(d)

Ans: (c)
Required distance

Q19: The distance between t he points (0, 0) and (a - b,  a + b) is    (2020)
(a)

(b)
(c)
(d)

Ans: (d)
Required distance =

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)

Ans: In rectangle AOBC. AB is a diagonal.

So,

= 5 Units

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

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

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)

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

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.

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)

(d)

Ans: (c)
Let the coordinates of centre of the circle be (x, y) and AB be the given diameter.
By Using mid-point formula.

We have,

∴ Coordinates of C are

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)

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.

By section formula, we have

Hence, the required point is  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)

Ans: We have, A(2, 5), B(x, y) and C(-1, 2) and point C divides AB in the ratio 3 :4.

∴ 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)

Ans:  Given AB = 5 units

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

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)

Ans: Let coordinates of the point A be (x, y) and O is the mid point of AB.

By using mid-point formula,
we have
⇒ -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)

Ans: Let the point R(x, 0) on x-axis divides the line segment PQ in the ratio k: 1.

∴ By section formula, we have

∴ 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)

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

Coordinates of P are  [By Section Formula]
Since, y-coordinate of P is 0
.
Hence, the point P divides the line segment in the ratio 3 : 5.
Also, x-coordinate of P
=
∴ 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)

Ans: Given,

∴ Coordinates of R are

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]

Ans: Let the coordinates of A be (x, y). Here, 0(3, - 1] is the mid point of AB.

By using mid point formula, we have⇒ 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)

Ans:
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

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)

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

∴ Coordinates of P are

The point P lies on line x - 3y = 0

∴ Required ratio is 13 : 3.Now, coordinates of P are

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)

Ans: Let the point P(-4, y) divides the line segment joining the points A and B in the ration k: 1

∴ By section formula, coordinates of P are

∴ Required ration is 2: 7.

Now,

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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## 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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