Question

On a coordinate plane, a line is drawn from point A to point B. Point A is at (9, negative 8) and point B is at (negative 6, 7).
What are the x- and y- coordinates of point P on the directed line segment from A to B such that P is Two-thirds the length of the line segment from A to B?

Answer 1

Vector from A to B = B − A = (−6 − 9, 7 − (−8)) = (−15, 15).
Two-thirds of that = (2/3)(−15, 15) = (−10, 10).
So P = A + (−10, 10) = (9 − 10, −8 + 10) = (−1, 2).

Answer: P = (−1, 2).