Question

$P(1,-2)$ is a point on the line segment $A(3,-6)$ and $B(x,y)$ such that AP$:$PB is equal to $2:3$. Find the coordinates of B.

Answer 1

As P is in between A&B, with the ratio known, we use Section formula.

$m:n=2:3$

$P_x=\frac{(x\times 2)+(3\times 3)}{2+3}$

$⟹1=\frac{2x+9}{5}$

$⟹x=-2$

Similarly, Use it to find y:

$y=4$

Thus $B:(-2,4)$