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Question

The medians AD and BE of a triangle with vertices A (0, b), B(0, 0) and C (a, 0) are perpendicular to each other, if


A

a=b2

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B

b=a2

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C

ab=1

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D

a=±2 b

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Solution

The correct option is D

a=±2 b


The midpoints of BC and AC are D(a2,0) and E(a2,b2)

Slope of AD =0ba20

Slope of BE =b2a2

It is given that the medians are perpendicular to each other.

0ba20×b2a2=1

a=±2b


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