Question

The line joining the points $(-6,8)$ and $(8,-6)$ is divided into four equal parts; find the coordinates of the points of section.

Answer 1

Let $A(-6,8)$ and $B(8,-6)$ and $P,Q,R$ divides $AB$ in four equal parts

$Q$ divides $AB$ in $1:1$, so $Q$ is the mid point of $AB$

So coordinates of $Q$ are $\frac{-6+8}{2},\frac{8-6}{2}$

$\Rightarrow Q(1,1)$

Similarly $P$ is the mid point of $AQ$

So, coordinates of $P$ are $\frac{-6+1}{2},\frac{8-1}{2}$

$\Rightarrow P(-\frac{5}{2},\frac{9}{2})$

$R$ is the mid point of $QB$

So, coordinates of $R$ are $\frac{1+8}{2},\frac{1-6}{2}$

$\Rightarrow R(\frac{9}{2},\frac{-5}{2})$

So, the coordinates of the points that divides the given points in four equal parts are $(-\frac{5}{2},\frac{9}{2});(1,1);\left(\frac{9}{2}\frac{-5}{2}\right)$