What is the endpoint formula for a line segment if you have one endpoint and a midpoint?

Answer 1

Suppose one end point is A and the midpoint is M.

Then the distance from the given end to the midpoint is M-A.

So the other end point is M-A further away from M ie it is at M + (M-A) = 2M-A.

The above answer looks like it is for 1 dimensional problems only but for two or more dimensions, either treat A and M as vectors or (if you are not familiar with vectors), apply the same rule to the x-coordinate, then separately, to the y-coordinate, etc.

So, in 2 dimensions,

if A = (ax, ay) and M = (mx, my)

then the other end point is (2mx- ax , 2my- ay)

and similarly for more dimensions.