Question

On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 8, negative 13) and point B is at (4, 11).
What are the x- and y- coordinates of point P on the directed line segment from A to B such that P is One-third the length of the line segment from A to B?

x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

(1, 5)
(0, 3)
(–4, –5)
(–5, –7)

Answer 1

Vector from A to B = (12, 24). One-third of that is (4, 8). Add to A: P = (-8+4, -13+8) = (-4, -5).

Answer: (–4, –5).