Question

The point P divides the join of (2,1) and (-3,6) in the ratio 2:3 . Dose P lie on the line $x-5y+15=0$ ?

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

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

Since, point P divides the join of (2,1) and (-3,6) in the ratio 2 : 3.

So, coordinates of P are :

$\left(\frac{2(-3)+3\left(2\right)}{5},\frac{2\left(6\right)+3\left(1\right)}{5}\right)=(0,3)$

If P lies on the given line, then it must satisfy the given equation of the line.

Therefore,

$x-5y+15=0$

$0-15+15=0$

$0=0$

Hence, point P lies on the given line.