Question

Find the point on the directed segment from (−2, 0) to (5, 8) that divides it in the ratio of 1: 3.

Answer 1

The answer to your question is (-1/3, 2)

Explanation:

Data

A (-2, 0)

B (5, 8)

ratio = 1/3

Formula

x =
`(x1 + rx2)/(1 + r)`

y =
`(y1 + ry2)/(1 + r)`

Substitution

x =
`(-2 + (1/3)(5))/(1 + 1/3)`

x = (-2 + 5/3) / (3 + 1) / 3

x = (-6 + 5)/3 / 4 / 3

x = - 1 / 3

y =
`(0 + (1/3)(8))/(1 + 1/3)`

y = (8 / 3) / (3 + 1) / 3

y = (8 / 3) / (4 / 3)

y = 8 / 4

y = 2

Point = (-1/3, 2)