What is the nature of the points (-a, -b),(0, | vedclass

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(A) Let the points be $A(-a, -b)$,$B(0, 0)$,$C(a, b)$,and $D(a^2, ab)$.To check if points are collinear,we check the slope between them.Slope of $AB =

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Collinear

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(A) Let the points be $A(-a, -b)$,$B(0, 0)$,$C(a, b)$,and $D(a^2, ab)$.To check if points are collinear,we check the slope between them.Slope of $AB = \frac{0 - (-b)}{0 - (-a)} = \frac{b}{a}$.Slope of $BC = \frac{b - 0}{a - 0} = \frac{b}{a}$.Since the slope of $AB$ is equal to the slope of $BC$,the points $A, B$,and $C$ are collinear.Now check the slope of $CD = \frac{ab - b}{a^2 - a} = \frac{b(a - 1)}{a(a - 1)} = \frac{b}{a}$ (for $a 
eq 1, 0$).Since the slopes of $AB, BC$,and $CD$ are all equal to $\frac{b}{a}$,all four points $A, B, C$,and $D$ lie on the same straight line.Therefore,the points are collinear.

What is the nature of the points $(-a, -b)$,$(0, 0)$,$(a, b)$,and $(a^2, ab)$?

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