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)=((mx_2+nx_1)/(m+n),(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)=((2\cdot2+3\cdot(-3))/(2+3),(2\cdot0+3\cdot(-10))/(2+3)) \\ =((4-9)/(5),(-30)/(5)) \\ (-(5)/(5),-6) \\ =(-1,-6) \end{gathered}`

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