Question

Find the coordinates of points which divide the line segment joining $A(-4,0)$ and $B(0,6)$ into four equal parts.

Answer 1

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

In the above image point $P$ divide the line segment into $1:3$

Now using section formula ,here $m=1,n=3$

$x_1=-4,x_2=0$ And $y_1=0,y_2=6$

$x_3=\frac{m{x}_1+n{x}_2}{m+n}$ , $y_3=\frac{m{y}_1+n{y}_2}{m+n}$

$x_3=\frac{1\left(0\right)+3(-4)}{3+1}=-3$,$y_3=\frac{1\left(6\right)+3\left(0\right)}{3+1}=1.5$

Similarly we can find the co-ordinates of $Q$, $R$

Co-ordinates of $Q$=$(-2,3)$ and co-ordinates of $R$=$(-1,4.5)$