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The 'e' Equation

Two sides of ...

Question

Two sides of a triangle are parallel to the coordinate axes. If the slopes of the medians through the acute angles of the triangle are $2$ and $m$ , then $m$ can be equal to

A

\frac{1}{2}

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B

2

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C

4

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D

8

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Solution

The correct options are
A $\frac{1}{2}$
D $8$
$m_{1}$ = slope of BD = $\frac{b + \frac{c}{2} - b}{a - (a + l)} = - \frac{c}{2 l}$
$m_{2}$ = slope of CE = $\frac{b - (b + c)}{a + \frac{l}{2} - a} = - \frac{2 c}{l}$
$∴ \frac{m_{1}}{m_{2}} = \frac{1}{4}$
$m_{1} = 2 \Rightarrow m_{2} = m = 8$
$m_{2} = 2 \Rightarrow m_{1} = m = \frac{1}{2}$

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