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Condition for Two Lines to Be Perpendicular

The medians A...

Question

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

A

b = \sqrt{2} a

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B

a = \sqrt{2} b

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C

b = - \sqrt{2} a

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D

a = - \sqrt{2} b

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Solution

The correct options are
C $a = \sqrt{2} b$
D $a = - \sqrt{2} b$
$F i n d o u t t h e c e n t r o i d G o f t h e Δ A B C b y u s i n g G = (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3}) T h e n t h e m e d i a n s a r e A G (o r A E) & B G (0 r B E) a n d t h e y a r e ⊥ e a c h o t h e r . ∴ m_{A G} \times m_{B G} = - 1$

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