Solveeit Logo
Login

Question

Question: The points \(( - a, - b),\mspace{6mu}(a,b),\mspace{6mu}(a^{2},ab)\) are....

The points (−a,−b), 6mu(a,b), 6mu(a2,ab)( - a, - b),\mspace{6mu}(a,b),\mspace{6mu}(a^{2},ab) are.

A

Vertices of an equilateral triangle

B

Vertices of a right angled triangle

C

Vertices of an isosceles triangle

D

Collinear

Answer

Collinear

Explanation

Solution

l1=(2a)2+(2b)2=2a2+b2l _ { 1 } = \sqrt { ( 2 a ) ^ { 2 } + ( 2 b ) ^ { 2 } } = 2 \sqrt { a ^ { 2 } + b ^ { 2 } }

l2=(a2−a)2+b2(a−1)2=(a−1)a2+b2l _ { 2 } = \sqrt { \left( a ^ { 2 } - a \right) ^ { 2 } + b ^ { 2 } ( a - 1 ) ^ { 2 } } = ( a - 1 ) \sqrt { a ^ { 2 } + b ^ { 2 } }

l3=(a2+a)2+b2(a+1)2=(a+1)a2+b2l _ { 3 } = \sqrt { \left( a ^ { 2 } + a \right) ^ { 2 } + b ^ { 2 } ( a + 1 ) ^ { 2 } } = ( a + 1 ) \sqrt { a ^ { 2 } + b ^ { 2 } }

Now l1+l2=l3l _ { 1 } + l _ { 2 } = l _ { 3 } Hence points are collinear.