Answer :
We have to find the coordinates of point P.
It is located in the segment AB and it is located such as the ratio AP:PB is 3:2.
We can think of the ratio as if the segment has 3+2=5 equally sized subsegments, where 3 subsegments are the distance from A to P and 2 subsegments are the distance from P to B:
As we have A and B located in certain coordinates of xy-plane, we can use the fact that P is goin to be 3/5 of the distance between AB in the x-coordinates and also in the y-coordinates, so we can calculate each coordinate separately:
[tex]x_p=x_a+\frac{3}{5}(x_b-x_a)=-5+\frac{3}{5}(5-(-5))=-5+\frac{3}{5}\cdot10=-5+6=1[/tex][tex]y_p=y_a+\frac{3}{5}(y_b-y_a)=-4+\frac{3}{5}(1-(-4))=-4+\frac{3}{5}\cdot5=-4+3=-1[/tex]The coordinates of P are
