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

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b=2a

a=±2b

b=−2a

a=−2b

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detailed solution

Correct option is B

The coordinates of D and E are (a/2, 0) and (a/2, b/2) respectively.Now, m1=Slope of AD=b−00−a/2=−2ba m2=Slope of BE=b/2−0a/2−0=baSince AD and BE are perpendicular. Therefore,m1m2=−1−2ba×ba=−1⇒a=±2b

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

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Ready to Test Your Skills?

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