Question

A segment with endpoints A (4, 2) and C (1, 5) is partitioned by a point B such that AB and BC form a 1:3 ratio. Find B.

(1, 2.5)
(2.5, 3.5)
(3.25, 2.75)
(3.75, 4.5)

Answer 1

The points are

A=(4,2)

C=(1,5)

Let point

B=(x,y)

Then,

the x-coordinates are in the ratio 1:3

AB/BC =(x-4)/(1-x)=1/3

Solving this equation in x

3x-12=1-x

4x=13

x=13/4=3.25

The y-coordinates are in the ratio 1:3

AB/BC =(y-2)/(5-y)=1/3

Solving this equation in y

3y-6=5-y

4y=11

y=11/4=2.75

The point
B is (3.25, 2.75)

This is option C