Let:
(x1,y1) = Initial point
(x2,y2) = End point
mp= midpoint = ((x1+x2)/2,(y1+y2)/2)
We know the midpoint and the endpoint, therefore:
(x1+x2)/2=14
(x1+13)/2 = 14
Solving for x1:
Multiply both sides by 2:
x1 + 13 = 28
Subtract 13 from both sides:
x1 = 15
And
(y1 + y2)/2 = 3
(y1 + (-6))/2 = 3
Solving for y1:
Multiply both sides by 2:
y1 - 6 = 6
Add 6 to both sides:
y1 = 12
Therefore the initial point is:
(x1,y1) = Initial point = (15, 12)