A, b, and c are collinear, and b is between a and c. the ratio of ab is 1: 1. if a is at (1,-9) and b is at (2,0), what are the coordinates of point c

(3,9)

Step-by-step explanation:

So I drew a right triangle with the line segment A(1,-9) to C as the hypotenuse.  This line segment does contain point B(2,0). This is shown in the picture.

We want to find a point C so that AB to BC has a ratio of 1:1. So this means B is the midpoint really.

So if we averaged the endpoints of the line segment it would equate to point B.

That is:

and

Multiply both sides by 2:

and

The first equation can be solved by subtracting 1 on both sides giving .

The second equation can be solved by adding 9 on both sides giving

.

Point C is (3,9).