Question
A, B, C are the three vertices of a triangle such that they are equidistant from the origin. A and B lie on the positive X and Y axes respectively and C lies on the line y + x = a. If AB = √2a, find the area of the triangle. (C lies in the first quadrant)
Answer: Option D
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D
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D
A and B are equidistant from origin and AB is √2a.
If we assume the points A and B to be (x,0) and (0,x) respectively,
AB= √x2+x2 = √2x = √2a
x=a
So A(0,a) and B(a,0) are the vertices.
Observe that A,B both lie on the line x+y=a and since C also lies on the line y+x = a, they are collinear.
Hence area of the triangle formed by the three points is 0.
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