Question

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

Answer 1

Answer:

(3,9)

Step-by-step explanation:

So I drew a right triangle with the line segment A(1,-9) to C$(a,b)$ 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$(a,b)$ 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:

$\frac{1+a}{2}=2$ and $\frac{-9+b}{2}=0$

Multiply both sides by 2:

$1+a=4$ and $-9+b=0$

The first equation can be solved by subtracting 1 on both sides giving $a=3$.

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

$b=9$.

Point C is (3,9).