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Question: The points \((a,b),\mspace{6mu}(c,d)\) and \(\left( \frac{kc + la}{k + l},\frac{kd + lb}{k + l} \rig...

The points (a,b), 6mu(c,d)(a,b),\mspace{6mu}(c,d) and (kc+lak+l,kd+lbk+l)\left( \frac{kc + la}{k + l},\frac{kd + lb}{k + l} \right) are.

A

Vertices of an equilateral triangle

B

Vertices of an isosceles triangle

C

Vertices of a right angled triangle

D

Collinear

Answer

Collinear

Explanation

Solution

The given points are collinear because the point (kc+lak+l,kd+lbk+l)\left( \frac { k c + l a } { k + l } , \frac { k d + l b } { k + l } \right) divides the points (a, b) and (c, d) in the ratio of k : l.