First slide

Equation of line in Straight lines

Question

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

Moderate

A

$b = \sqrt{2} a$
B

$a = \pm \sqrt{2} b$
C

$b = - \sqrt{2} a$
D

$a = - 2 b$

Solution

The coordinates of $D$ and $E$ are $(a / 2, 0)$ and $(a / 2, b / 2)$ respectively.
Now, $m_{1} =$ Slope of $A D = \frac{b - 0}{0 - a / 2} = - \frac{2 b}{a}$
$m_{2} =$ Slope of $B E = \frac{b / 2 - 0}{a / 2 - 0} = \frac{b}{a}$
Since $A D$ and $B E$ are perpendicular. Therefore,
$m_{1} m_{2} = - 1 - \frac{2 b}{a} \times \frac{b}{a} = - 1 \Rightarrow a = \pm \sqrt{2} b$

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