Question

The points (–a, –b), (0, 0), (a, b) and (a^2, ab) are

• A. vertices of a rectangle
• B. vertices of a parallelogram
• C. collinear
• D. none of these

Answer 1

The correct option is C collinear

$LetA\equiv (-a,-b),B\equiv (0,0)c\equiv (a,b)andD\equiv (a^2,ab)Then,slopeofAB=\frac{b}{a},slopeofBC=\frac{b}{a}andslopeofCD=\frac{ab-b}{a^2-a}=\frac{b(a-1)}{a(a-1)}=\frac{b}{a}$
Thus, the points A, B, C and D are collinear