CAT 2025 Coordinate Geometry Question (Hard)

Question

The x, y coordinates of vertices , 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

Accepted Answer

Given P -3,-2 , Q 1,-5 , and R 9,1 . For parallelogram PQRS , S P R - Q -3,-2 9,1 - 1,-5 5,4 Diagonal SQ passes through S 5,4 and Q 1,-5 . Slope m 1-5 4 Equation of SQ is y - 4 4 x - 5 At the x-axis, y 0 -4 4 a - 5 -16 9 a - 5 9a 29 a 9 So, a 9

CAT 2025

Quantitative

Coordinate Geometry

Hard

The ((x, y)) coordinates of vertices (\mathrm{P}, \mathrm{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

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