Question

The points $(-a,-b),(a,b),(0,0)$ and $(a^2,ab),a\ne 0,b\ne 0$ are

• A. Collinear
• B. Vertices of a parallelogram
• C. Vertices of rectangle
• D. Lie on a circle

Answer 1

The correct option is A Collinear

Let the points are $A(-a,-b),B(a,b),C(0,0)$ and $D(a^2,ab)$, then

slope of line $AB=\frac{b}{a}=$ slope of line $BC=$ slope of line $CD=$ slope of line $DA$

Hence all the given $4$ points are collinear.

Note: Slope of line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $\frac{y_2-y_1}{x_2-x_1}$