Question

What are the coordinates of point B on Line AC such that AB is 3 times as long as BC? (Screenshots supplied to clarify)

Answer 1

(3.5, 0.5) or A

Explanation:

Got it right

Answer 2

B(3.5, 0.5)

Explanation:

Given:

A(5,5), Xa=5, Ya=5

C(3,-1), Xc=3, Yc=-1

To find point B, we can use the partition rule, where AB = 3BC, so AB occupies k=3/4 of the distance AC.

B(x,y) = ((1-k)Xa+kXc, (1-k)Ya+kYc)

=(Xa/4+3Xc/4, Ya/4+3Yc/4), substitute values

=(5/4+3*3/4, 5/4+3*(-1)/4)

=(14/4,2/4)

=(3.5, 0.5)