Question

The points (3a, 0), (0, 3b) and (a, 2b) are.

• A. Vertices of an equilateral triangle
• B. Vertices of an isosceles triangle
• C. Vertices of a right angled isosceles triangle
• D. Collinear

Answer 1

Answer: (D)

Collinear

Answer 2

$l _ { 1 } = \sqrt { ( 3 a ) ^ { 2 } + ( 3 b ) ^ { 2 } } = 3 \sqrt { a ^ { 2 } + b ^ { 2 } }$

$l _ { 2 } = \sqrt { a ^ { 2 } + b ^ { 2 } } = \sqrt { a ^ { 2 } + b ^ { 2 } }$

$l _ { 3 } = \sqrt { ( 2 a ) ^ { 2 } + ( 2 b ) ^ { 2 } } = 2 \sqrt { a ^ { 2 } + b ^ { 2 } }$ $\Rightarrow l _ { 1 } = l _ { 2 } + l _ { 3 }$

Hence the points are collinear.