Question

CD has the endpoints C(3, 2) and D(–5, –2). Charlie wants to place the point E at the point that partitions this line segment in a 3:1 ratio. What are the coordinates of the point E?

(
,
)

Answer 1

CE:ED = 3:1 so E is 3/4 of the way from C to D.

Vector D − C = (−5 − 3, −2 − 2) = (−8, −4).
E = C + (3/4)(D − C) = (3, 2) + (3/4)(−8, −4) = (3 − 6, 2 − 3) = (−3, −1).

(−3, −1)