SOLUTION: The midpoint of segment AB is (0,1/2). if endpoint A is (2,-2), find the coordinates of endpoint B.

Graphical method:

Call the midpoint 



Draw a green line from A(2,-2) left horizontally until you 
are directly underneath the midpoint .  That 
requires you to draw the green line 2 units left.  



Now from the end of the green line, draw a vertical 
green line upward to point . That 
requires you to draw the vertical green line  units 
directly upward.  




Draw a green line from  left 2 units 
horizontally, the same number of units left that we
drew the other horizontal line. That puts you directly
above -2 on the x-axis.

 

Now from the end of that green line, draw a green line 
directly upward  units vertically, the same 
number of units left that we drew the other vertical 
line. That puts you directly above -2 on the x-axis.



Now we can extend AM to B, and we now have AB.  And we see 
that B is the point B(-2,3)



By algebra:

Use the midpoint formula:

The midpoint between  and 

is 

So

The midpoint between  and 

is 

So



So we set the x-coordinates equal:



Multiply both sides by 2





And we set the y-coordinates equal:



Multiply both sides by 2





So B has the coordinates 

Edwin