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)

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol