Question

Find the coordinates of point B on line AC such that AB is 1/3 of AC.

I have tried everything, I would really appreciate someone's input on this, thank you.

Answer 1

The coordinates of B are (3, -1).

Explanation:

Here's one possible, straightforward way in which you can identify the point B:

Notice that in going straight up from A to C, y increases by 12 units.

Going to the right from A to C, x increses by 3 units.

The x-coordinate of B is (x-coordinate of A) + (1/3)(increase in x going from A to B). Thus, the x-coord. of B is (2 + [1/3][3]) = 2 + 1 = 3.

The y-coord. of B is (y-coord. of A + 1/3(increase in y going from A to B), or -5 + (1/3)[12]) = -5 + 4 = -1.

So the coordinates of B are (3, -1).