Question

Given that $A(5,4),B(-3,-2)$ and $C(1,-8)$ are the vertices of a $△ABC$
Find:
i)The slope of median $AD$,
ii) The slope of altitude $BM$.

Answer 1

Consider the following question.

i)The slope of median AD

ii) The slope of altitude BM.

$A(5,4),B(-3,-2)\&C(1,-8)$

Hence, D & M is the mid point of BC & AC.

$D=(\frac{5-3}{2},\frac{4-2}{2})$

$D=(1,1)$

$=1$

$M=(\frac{-3+1}{2},\frac{-2-8}{2})$

$M=(-1,-5)$

Slope of AD

$AD=\left(\frac{1-4}{1-5}\right)$

$=-\frac{3}{4}$

Slope of BM.

$BM\left(m_1\right)=\left(\frac{-2+5}{-3+1}\right)$

$=-\frac{3}{2}$

The slope of altitude BM

$m_1\times m_2=-1$

$m_2=\frac{1}{-m_1}$

$=\frac{1}{-\left(\frac{-3}{2}\right)}$

$=\frac{2}{3}$

Hence, this is the required answer.