First slide

Cartesian plane

Question

The points $P (a, b), Q (c, d), R (a, d)$ and $S (c, b),$ where $a, b, c,$ dare distinct real numbers, are

Easy

A

collinear
B

vertices of a square
C

vertices of a rhombus
D

concyclic

Solution

We have,
Slope of $P S = 0 =$ Slope of $Q R$
and,
Slope of $P R = \infty =$ Slope of $Q S$
$\Rightarrow P S$ and $Q R$ are parallel to $x -$ axis and $P R$ and $Q S$ are parallel to $y -$ axis.
$\Rightarrow P Q R S$ is a rectangle.
Also, $P Q = R S .$
Hence, $P Q R S$ is a square.

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