Question

If the vertices of a triangle are A(-a, b), B(-a, c) and C(a, c), then the area of triangle = sq units.

• A. b(a-c)
• B. a(c-b)
• C. c(b-a)

Answer 1

The correct option is B a(c-b)


A and B lie on the line x = -a and 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.
$\because$ Distance between points on a line parallel to X - axis is difference of x- coordinates
$\therefore$ BC = |difference of x- coordinates|
= 2a
$\because$ Distance between points on a line parallel to Y - axis is difference of y- coordinates
$\therefore$ AB = |difference of y- coordinates|
= c - b.
When AB is the base, BC is the height.
Area of the triangle $=\frac{1}{2}\left[2a\right(c-b\left)\right]=a(c-b)$