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
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B
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C
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D
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Solution
The correct option is D The coordinates of the middle points D and E are D≡(a2,0),E≡(a2,b2) Slope of median AD is m1=−2ba slope of median BE is m2=−ba since AD⊥BE ∴m1×m2=−1⇒−2ba×ba =−1⇒a=±√2b