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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.
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B
Area of the triangle = b(a - c)
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C
The triangle is equilateral.
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D
Area of the triangle = a(c - b)
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Solution

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 =12[Base×Height]
Area of the triangle =12[(cb).2a]=a.(cb)


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