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

Section formula :
Any point let say $(x,y)$ divides the line joining points $(x_1,y_1)$ & $(x_2,y_2)$ in the ratio $m:n$, then co-ordinates were given by the formula
$x=\frac{x_1\times n+x_2\times m}{m+n}$

$y=\frac{y_1\times n+y_2\times m}{m+n}$

Given points $A(-6,8)$ and $B(8,-6)$
(i) Point $P(x,y)$ divides $AB$ in the ratio $1:3$
$x=\frac{(-6)\times 3+\left(8\right)\times 1}{1+3}=\frac{-5}{2}$
$y=\frac{8\times 3+(-6)\times 1}{1+3}=\frac{9}{2}$
Then, $P(\frac{-5}{2},\frac{9}{2})$
(ii) Point $Q(x,y)$ divides $AB$ in the ratio $2:2=1:1$
$x=\frac{(-6)\times 1+\left(8\right)\times 1}{1+1}=1$
$y=\frac{8\times 1+-6\times 1}{1+1}=1$
Then, $Q(1,1)$
(iii) Point $R(x,y)$ divides $AB$ in the ratio ratio $3:1$
$x=\frac{(-6)\times 1+\left(8\right)\times 3}{1+3}=\frac{9}{2}$
$y=\frac{8\times 1+(-6)\times 3}{1+3}=\frac{-5}{2}$
Then, $R(\frac{9}{2},\frac{-5}{2})$