A(-2,-2) and B(5,7) are the endpoints of line AB. point C lies on line AB and is 1/3 of the way from B to A. what is the y-coordinate of point C

Answer 1

The derivation of the formula for this is a nuisance which I can't easily show you here, but the answer is

x: (2/3)5 + (1/3)(-2) = (10/3)-(2/3)= 8/3

y: (2/3)7 + (1/3)(-2)= (14/3)-2/3 = 4

If you plot this on graph paper, you will see that it is correct.

If you want to develop this formula for yourself, start with a right triangle and draw lines parallel to the legs in the proportion required. Then some reasonably simple geometry will get you the result.