CAT 2025 Slot 1 QA Question 1: 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

Question

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

Accepted Answer

For a parallelogram, diagonals bisect each other. Hence, if P, Q, R and S are consecutive vertices,
$P + R = Q + S$
$S = P + R - Q$
$S = (-3, -2) + (9, 1) - (1, -5) = (5, 4)$

So, the diagonal SQ passes through $S(5, 4)$ and $Q(1, -5)$. Its slope is
$m = \dfrac{-5 - 4}{1 - 5} = \dfrac{9}{4}$

Using

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

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