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. $\Delta ABC$ is a right angled triangle, right angled at A.
• B. Area of the triangle = b(a - c)
• C. The triangle is equilateral.
• D. Area of the triangle = a(c - b)

Answer 1

The correct option is D Area of the triangle = a(c - b)

Observe that A and B lie on the line x = -a
The points B and C lie on the line y = c.
Since these lines x = -a and y = c are parallel to the Y and X axes respectively, these lines (x = -a and y = c ) are perpendicular to each other.

Hence it is right angled at B.

BC = 2a, AB = c - b.
When AB is the base, BC is the height.

Area of the triangle $=\frac{1}{2}[Base\times Height]$
$\therefore$ Area of the triangle $=\frac{1}{2}\left[\right(c-b).2a]=a.(c-b)$