CLASS X Math - Previous Year Question
Coordinate Geometry
Q1. The distance between the points
(𝑎 cos 𝜃 + 𝑏 sin 𝜃, 0) and (0, 𝑎 sin 𝜃 − 𝑏 cos 𝜃) is [2020] [1 Marks]
(a) 𝑎2 + 𝑏 2 (b) 𝑎2 − 𝑏 2 (c) √𝑎2 + 𝑏 2 (d) √𝑎2 − 𝑏 2
Q2. 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] [1 Marks]
(a) 1 (b) 2 (c) −2 (d) −1
Q3. If A(3, √3), 𝐵(0,0) and 𝐶(3, 𝑘) are the three vertices of an equilateral
triangle ABC, then the value of 𝑘 is [2021] [1 Marks]
(a) 2 (b) −3 (c) −√3 (d) −√2
Q4. Three vertices of a parallelogram ABCD are A(1, 4), B(-2, 3), and C(5, 8). The
ordinate of the fourth vertex D is [2021] [1 Marks]
(a) 8 (b) 9 (c) 7 (d) 6
Q5. Points A(-1, y) and B(5, 7) lie on a circle with centre O(2,-3y). The values of y
are [2021] [1 Marks]
(a) 1, − 7 (b) −1, 7 (c) 2, 7 (d) −2, − 7
Q6. If A (4, -2), B (7, -2) and C (7, 9) are the vertices of a ∆𝐴𝐵𝐶, then ∆𝐴𝐵𝐶 is
[2021] [1 Marks]
(a) Equilateral triangle (b) isosceles triangle
(c) right-angle triangle (d) isosceles right-angle triangle
Q7. The line segment joining the points P(-3, 2) and Q(5, 7) is divided by the y-
axis in the ratio [2021] [1 Marks]
(a) 3: 1 (b) 3: 4 (c) 3: 2 (d) 3: 5
Q8. The ratio in which the line 3𝑥 + 𝑦 − 9 = 0 divides the line segment joining
the points (1, 3) and (2, 7) is [2021] [1 Marks]
(a) 3: 2 (b) 2: 3 (c) 3: 4 (d) 4: 3
Q9. The base BC of an equilateral ∆𝐴𝐵𝐶 lies on y-axis. The co-ordinates of C are
(0, -3). If the origin is the mid-point of the base BC, what are the co-ordinates of
A and B? [2021] [1 Marks]
(a) 𝐴(√3, 0), 𝐵(0,3) (b) 𝐴(±3√3, 0), 𝐵(3,0)
(c) 𝐴(±3√3, 0), 𝐵(0,3) (d) 𝐴(−√3, 0), 𝐵(3,0)
Q10. The distance of the point (-1, 7) from x-axis is: [2023] [1 Marks]
(a) −1 (b) 7 (c) 6 (d) √50
3
Q11. The mid-point of the line segment joining the point (-1,3) and (8, ) is
2
[2024] [1 Marks]
7 3 7 9 9 3 7 9
(a) ( , − ) (b) ( , ) (c) ( , − ) (d) ( , )
2 4 2 2 2 4 2 4
Q12. The distance between the points (2,-3) and (-2,3) is [2024] [1 Marks]
(a) 2√13 Units (b) 5 units (c) 13√2 units (d) 10 units
Q13. The diameter of a circle is of length 6 cm. If one end of the diameter is
(-4,0), the other end on x-axis is at: [2024] [1 Marks]
(a) (0,2) (b) (6,0) (c) (2,0) (d) (4,0)
Q14. Find the distance of a point 𝑃(𝑥, 𝑦) from the origin. [2018] [1 Marks]
Q15. Find the coordinates of a point A, where AB is diameter of a circle whose
centre is (2, −3) and B is the point (1, 4). [2019] [1 Marks]
Q16. Find the ratio in which P (4, m) divides the line segment joining the points
A (2, 3) and B (6, –3). Hence find m. [2018] [2 Marks]
Q17. Find the ratio in which the segment joining the points (1, – 3) and (4, 5)
is divided by x-axis? Also find the coordinates of this point on x-axis. [2019] [2
Marks]
Q18. If A (–2, 1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram
ABCD, find the values of a and b. Hence find the lengths of its sides. [2018] [3
Marks]
Q19. Find the co-ordinates of the points of trisection of the line segment joining
the points (-2, 2) and (7, -4). [2024] [3 Marks]
Q20. Find the point on y-axis which is equidistant from the points (5, − 2) and
(−3, 2). [2019] [3 Marks]
Q21. 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 line given by
2𝑥 − 𝑦 + 𝑘 = 0, find the value of 𝑘. [2019] [3 Marks]
Q22. 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] [3 Marks]
Q23. Case Study [2023] [4 Marks]
Jagdish has a field which is in the shape of a right angled trainagle 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.
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)?
