Answer:
C(-3,3)
Explanation:
Given
A = (7,-1)
B = (2,1)
AB:AC = 1:2
Required
Determine the coordinates of C
Since, B is between A and C; we need to determine ratio BC as follows;

Convert to division

AC = AB + BC;

Cross Multiply




Divide both sides by BC

Rewrite as

Write as ratio

Next is to determine the coordinates of C as follows;
Because B is between both points. we have:

Where



So; we're solving for x2 and y2

Where
Solving for x2;



Cross Multiply




Solving for y2;



Cross Multiply




Hence, the coordinates of C are: C(-3,3)