Question

Given the points A (-4,-2) and B (4, 10), find the

coordinates of point P on directed line segment AB that is 3/4 is of the way from A to B.

Answer 1

P = (2, 7)

Explanation:

You want to find coordinates of P on segment AB such that P is 3/4 is of the way from A to B.

Equation for P

For some fraction q of the distance from A to B, the point P that lies at that fraction of the distance is given by ...

P = A +q(B -A) = (1 -q)A +qB

Application

For q = 3/4, the location of P is ...

P = (1 -3/4)A + 3/4B = (A +3B)/4

Using the given point coordinates, we have ...

P = ((-4, -2) +3(4, 10))/4 = (-4 +12, -2 +30)/4 = (8, 28)/4

P = (2, 7)