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

Answer 1

Answer:

$C = (\frac{33}{5},\frac{19}{5})$

Step-by-step 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:

$C = (\frac{nx_1 + mx_2}{n+m},\frac{ny_1 + my_2}{n+m})$

Where:

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

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

$m:n = 4 : 1$

So:

$C = (\frac{1 * 1 + 4*8}{1+4},\frac{1*3 + 4*4}{1+4})$

$C = (\frac{33}{5},\frac{19}{5})$