First slide

Cartesian plane

Question

The points $(- x, - y), (0, 0), (x, y), (x^{2}, x y)$ are

Moderate

A

The vertices of a rectangle
B

The vertices of a square
C

The vertices of rhombus
D

Collinear

Solution

$A (- x, - y), B (0, 0), C (x, y), D (x^{2}, x y)$
Slope of $A B = \frac{y}{x},$ slope of $B C = \frac{y}{x}$

Slope of $\bar{C D} = \frac{x y - y}{x^{2} - x} = \frac{y (x - 1)}{x (x - 1)} = \frac{y}{x}$

$∴$ A,B,C,D are collinear

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