CAT Coordinate Geometry questions (1991–2025) — actual Quant questions with solutions

Visual Lens | Coordinate Geometry | MEDIUM

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

Coordinate + InCircle

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

The coordinates of a triangle are (1, 2), (7, 2), and (1, 10). Find the inradius.

In the XY-plane, the area, in sq. units, of the region defined by the inequalities y ≤ x + 4 and −4 ≤ x² + y² + 4(x − y) ≤ 0 is.

Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates o the vertex D are

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

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

The area, in sq. units, enclosed by the lines x = 2, y = |x – 2| + 4, the X-axis and the Y-axis is equal to

Let S be the set of all points (x, y) in the x-y plane such that |x| + |y| ≤ 2 and |x| ≥ 1. Then, the area, in square units, of the region represented by equals

Let T be the triangle formed by the straight line 3x + 5y − 45 = 0 and the coordinate axes. Let the circumcircle of T have radius of length L, measure in the same unit as the coordinate axes. Then, the integer closest to L is

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 th point (0, 0) is

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

The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is

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) coordinate The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

The area of the triangle with the vertices (a, a), (a + 1, a) and (a, a + 2) is

The area bounded by the three curves |x + y| = 1, |x| = 1, and |y| = 1, is equal to

There are two straight lines in the x-y plane with equations ax + by = c , dx + ey = f. Do the two straight lines intersect? a, b, c, d, e and f are distinct real numbers. c and f are non-zero.

The robot reaches point (6, 6) when a sequence of three instructions is executed, the first of which is a GOTO(x,y) instruction, the second is WALKX(2 and the third is WALKY(4). What are the value of x and y?

The robot is initially at (x, y), x > 0 and y < 0. The minimum number of instructions needed to be executed to bring it to the origin (0, 0) if you ar prohibited from using the GOTO instruction is

What is the distance between the points A(3, 8) and B(–2, –7)?