Question

- 2. Given the point A (-3,-10) and B (2,0), find the coordinates of the point P on directed line segment AB that partition AB in the ratio 2 to 3.

Answer 1

The point P divide the line segement AB in 2:3 ratio.

The point are A(-3,-10) and B(2,0).

The formula for the coordinates of the point that divide the segment A(x_1,y_1) and (x_2,y_2) in ratio m:n.

$(x,y)=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

For the given problem m = 2 and n = 3.

Substitute the given values in the formula to obtain the coordinates of point P.

$\begin{gathered} P(x,y)=(\frac{2\cdot2+3\cdot(-3)}{2+3},\frac{2\cdot0+3\cdot(-10)}{2+3}) \\ =(\frac{4-9}{5},\frac{-30}{5}) \\ (-\frac{5}{5},-6) \\ =(-1,-6) \end{gathered}$

So coordinates of point P is (-1,-6).