Remark
There are two formulas for doing this. I'll use the one that does not involve the slope. I think it will be easier for you to understand.
Step One
Decide which point is (x1,y1)
Since point P is 2/5 the way up from point A, we will call (x1,y1) point A
Step Two
Write the givens.
Point(A) = (-2,-3)
Point(B) = (3,2)
Step Three
Write the formula
x1 + ratio*(x2 - x1), y1 + ratio(y2 - y1)
Sub and solve.
-2 + 2/5 *(3 - - 2) , -3 + 2/5*(2 - -3)
-2 + 2/5(5) , - 3 + 2
-2 + 2 , - 1
P = (0 , - 1) <<<<<< Answer
If this turns out to be incorrect please notify me.
