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?

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

(2, –1)
(4, –3)
(–1, 2)
(3, –2)

Answer 1

Compute P = A + (2/3)(B − A).

B − A = (−6 − 9, 7 − (−8)) = (−15, 15).
(2/3)(B − A) = (−10, 10).
P = (9 − 10, −8 + 10) = (−1, 2).

Answer: (−1, 2).