Question

On a coordinate plane, a line is drawn from point A to point B. Point A is at (2, negative 3) and point B is at (negative 4, 9).
What are the x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2?

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

(0, 1)
(–1, 3)
(–2, 5)
(1, 0)

Answer 1

Use m:n = 1:2 so m/(m+n) = 1/3.

x = 1/3(x2 − x1) + x1 = 1/3(−4 − 2) + 2 = 1/3(−6) + 2 = 0
y = 1/3(y2 − y1) + y1 = 1/3(9 − (−3)) − 3 = 1/3(12) − 3 = 1

So E = (0, 1).