CAT Coordinate Geometry Questions & Solutions

A sample of real CAT Coordinate Geometry past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 17 Coordinate Geometry questions in all — sign up free to practise them timed.

1. Q1.CAT 2025

   The (x, y) coordinates of vertices P, Q and R of a parallelogram PQRS are (-3, -2), (1, -5) and (9, 1), respectively. If the diagonal SQ intersects the x-axis at (a, 0) , then the value of a is

   • $\dfrac{27}{7}$

   • $\dfrac{10}{3}$

   • $\dfrac{13}{4}$

   • $\dfrac{29}{9}$

2. Q2.CAT 2024

   The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the incircle of the triangle is

   Answer: 2

3. Q3.CAT 2023

   Let C be the circle $x^{2} + y^{2} + 4x - 6y - 3 = 0$ and L be the locus of the point of intersection of a pair of tangents to C with the angle between the two tangents equal to $60^{\circ}$. Then, the point at which L touches the line $x$ = 6 is

   • (6, 6)

   • (6, 3)

   • (6, 8)

   • (6, 4)

4. Q4.CAT 2020

   The points (2,1) and (-3,-4) are opposite vertices of a parallelogram.If the other two vertices lie on the line $x+9y+c=0$, then c is

   • 12

   • 13

   • 15

   • 14

5. Q5.CAT 2020

   The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is

   • $\frac{14\pi}{3}$

   • $\frac{123\pi}{7}$

   • $\frac{12\pi}{5}$

   • $\frac{205\pi}{9}$

6. Q6.CAT 2018

   Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will be

   • $188\sqrt{3}$

   • $248\sqrt{3}$

   • $164\sqrt{3}$

   • $192\sqrt{3}$

7. Q7.CAT 2018

   A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is

   • $8$ units

   • $4$ units

   • $2\sqrt{2}$ units

   • $4\sqrt{2}$ units

8. Q8.CAT 2017

   The area of the closed region bounded by the equation

   I x I + I y I = 2 in the two-dimensional plane is

   • $4\pi$ sq. units

   • 4 sq. units

   • 8 sq. units

   • $2\pi$ sq. units

9. Q9.CAT 2017

   The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y =3x+c,then c is

   • -5

   • -6

   • -7

   • -8

10. Q10.CAT 2005

    Consider a triangle drawn on the X-Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X,Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

    • 780

    • 800

    • 820

    • 741

11. Q11.CAT 2000

    ABCD is a rhombus with the diagonals AC and BD intersection at the origin on the x-y plane. The equation of the straight line AD is x + y = 1. What is the equation of BC?

    • $x+y=-1$

    • $x-y=-1$

    • $x+y=1$

    • None of the above

12. Q12.CAT 1996

    The points of intersection of three lines $2x+3y-5=0, 5x-7y+2=0$ and $9x-5y-4=0$

    • form a triangle

    • are on lines perpendicular to each other

    • are on lines parallel to each other

    • are coincident

CAT Coordinate Geometry previous year questions with solutions — AthenaPrep