A, b, and c are collinear, and B is between a and c. The ratio of AB to AC is 1:2. If A is at (7,-1) and B is at (2,1) what are the coordinates of point C

C(-3,3)

Step-by-step 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)

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