Question

Find the coordinates of the point $P$, which divides the join of $A(-2,5)$ and $B(3,-5)$ in the ratio $2:3$.

Answer 1

Let $P(x,y)$ divide the line $A(-2,5)$ and $B(3,-5)$ in the ratio $2:3$.

Using section formula,

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

where $m=2,n=3,x_1=-2,y_1=5,x_2=3,y_2=-5$

$P(x,y)=(\frac{2\times 3+3\times -2}{2+3},\frac{2\times -5+3\times 5}{2+3})$

$=(\frac{6-6}{5},\frac{-10+15}{5})=(0,\frac{5}{5})$

$=(0,1)$

$\therefore$ The point $(0,1)$ divides the line $AB$