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

The correct option is D

Collinear

$I_1=\sqrt{(3a{)}^2+(3b{)}^2}=3\sqrt{a^2+b^2}$

$I_2=\sqrt{a^2+b^2}=\sqrt{a^2+b^2}$

$I_3=\sqrt{(2a{)}^2+(2b{)}^2}=2\sqrt{a^2+b^2}\Rightarrow I_1=I_2+I_3$

Hence the points are collinear.