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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)
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B
a(c-b)
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C
c(b-a)
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Solution

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.
Distance between points on a line parallel to X - axis is difference of x- coordinates
BC = |difference of x- coordinates|
= 2a
Distance between points on a line parallel to Y - axis is difference of y- coordinates
AB = |difference of y- coordinates|
= c - b.
When AB is the base, BC is the height.
Area of the triangle =12[2a(cb)]=a(cb)

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