Question

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

Answer 1

Given, $A(5,4),B(-3,-2)$ and $C(1,-8)$ are the vertices of a triangle ABC.

Also, D is the mid-point of BC.

We know, midpoint of $B(x_1,y_1)$ and $C(x_2,y_2)$ is given by:
$=[\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}]$

$\therefore \text{Co-ordinates of point}D=(\frac{-3+1}{2},\frac{-2-8}{2})$

$=(-1,-5)$

Now, the slope of $A(x_1,y_1)$ and $D(x_2,y_2)$ is given by:
$=\frac{y_2-y_1}{x_2-x_1}$

$\therefore \text{Slope of}AD=\frac{-5-4}{-1-5}$

$=\frac{-9}{-6}$

$=\frac{3}{2}$

Hence, the slope of the median AD is $\frac{3}{2}$.