Question

A directed line segment AB with A (1,3) and B (8,4) is partitioned by point C such that AC and CB form a 4:1 ratio. Find C

Write your answer as a coordinate point.
Do not include spaces in your answer.
Write your answer as a decimal if necessary.

Answer 1

`C = ((33)/(5),(19)/(5))`

Explanation:

Given

`A = (1,3)`

`B = (8,4)`

`AC : BC = 4 : 1`

Required

Determine the coordinates of C

To do this, we make use of:

`C = ((nx_1 + mx_2)/(n+m),(ny_1 + my_2)/(n+m))`

Where:

`A = (1,3)` ----
`(x_1,y_1)`

`B = (8,4)` ----
`(x_2,y_2)`

`m:n = 4 : 1`

So:

`C = ((1 * 1 + 4*8)/(1+4),(1*3 + 4*4)/(1+4))`

`C = ((33)/(5),(19)/(5))`