how do you find the endpiong of a segment given the endpiont and the midpiont

First, imagine the following segment:

If you know the endpoint A and the midpoint B, then finding the other endpoint C is easy.

You would first have to find the change in X (ΔX) and change in Y (ΔY)when moving from point A to point B.

Lets give point A the coordinates (2,4) and point B the coordinates (5,8).

To find ΔX we subtract the X coordinate in point B from point A: ΔX=5-2=3 ΔX=3

To find ΔY we subtract the Y coordinate in point B from point A: ΔY=8-4=4 ΔY=4

To verify, simply add the ΔX and ΔY to the point A coordinates and you will get the coordinates of point B. 2+3=5 and 4+4=8

Since B is the midpoint, the distance between A and B is equal to the distance between B and C, which means the ΔX and ΔY are the same.

So take the coordinates of point B and add the ΔX and ΔY: 5+3=8 and 8+4=12

With that we find that the coordinates of point C are (8,12)

Nice answer AT....!!!

Here's another way.....

Notice that the midpoint "formula" is just ( [x₁ + x₂] / 2 , [y₁ + y₂ ] / 2  )....So, let's suppose we know (x₁, y₁)  and the midpoint - call it (m₁, m₂). Then, to find the other endpoint, (x₂, y₂),  we have (2m₁ - x₁ ,  2m₂ - y₁). The process would work in a similar manner if we were trying to find (x₁, y₁).

Basically, we're just "manipulating" the midpoint formula to find an unknown......!!!!

Hope that helps......