Question

The points A(-a,b), B(-a,c) and C(a,c) form the vertices of a triangle. Which of the following is true?

• A. ΔABC is a right angled triangle, right angled at A.
• B. Area of the triangle = b(a-c)
• C. ΔABC is a right angled triangle, right angled at C.
• D. Area of the triangle = a(b-c)

Answer 1

The correct option is D

Area of the triangle = a(b-c)

By plotting the given points on a graph as shown, we see that the triangle is right angled at B.

Distance $BC=2a$

Distance $AB=b–c$

Area $=\frac{1}{2}\times BC\times AB$

= $\frac{1}{2}\times 2a\times (b-c)$

=$a(b-c)$