Question

If the vertices of triangle are (0,2), (1,0) and (3,1), then the triangle is.

• A. Equilateral
• B. Isosceles
• C. Right angled
• D. Isosceles right angled

Answer 1

Answer: (D)

Isosceles right angled

Answer 2

Here $A ( 0,2 ) , B ( 1,0 )$ and $C ( 3,1 )$

Therefore, $A B = \sqrt { 1 + 4 } = \sqrt { 5 } , B C = \sqrt { 4 + 1 } = \sqrt { 5 }$

and $A C = \sqrt { 9 + 1 } = \sqrt { 10 }$

It is clear that $( A C ) ^ { 2 } = ( A B ) ^ { 2 } + ( B C ) ^ { 2 }$

Hence, triangle is isosceles right angled.