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Question

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

A
b=2a
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B
a=2b
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C
b=2a
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D
a=2b
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Solution

The correct options are
B a=2b
D a=2b
Given vertices
A(0,b),B(0,0).C(a,0) are mutually perpendicular
According to the given figure,
The slope(AD)=ba/2=m1
The slope (BE)=b/2a/2=b2=m2
For it to be rt>m1m2=1
Or 2ba×ba=1
Or a2=2b2
a=±2b
ie a=2b
Or
a=2b


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