Learn how to find an endpoint using the midpoint of a segment with a couple of good examples.
Example #1:
The midpoint of a segment is M(2, 3). One endpoint is A(-2, -1). Find the other coordinates of the other endpoint B.
Use the midpoint formula M[(x1 + x2)/2, (y1 + y2)/2] and let the coordinates of B be (x2, y2)
Notice that (x1 + x2)/2 is the x-coordinate of the midpoint. So (x1 + x2)/2 = 2
Notice that (y1 + y2)/2 is the y-coordinate of the midpoint. So (y1 + y2)/2 = 3
Let x1 = -2 and y1 = -1 and solve the two equations below:
(-2 + x2)/2 = 2 and (-1 + y2)/2 = 3
Solve (-1 + y2)/2 = 3
Multiply both sides of (-1 + y2)/2 = 3 by 2
2(-1 + y2)/2 = 3(2)
Simplify
-1 + y2 = 6
Add 1 to both sides of the equation
-1 + 1 + y2 = 6 + 1
Simplify
y2 = 7
Solve (-2 + x2)/2 = 2
Multiply both sides of (-2 + x2)/2 = 2 by 2
2(-2 + x2)/2 = 2(2)
Simplify
-2 + x2 = 4
Add 2 to both sides of the equation
-2 + 2 + x2 = 4 + 2
Simplify
x2 = 6
The coordinates other endpoint B are (6, 7)
Example #2:
The midpoint of a segment is M(-1, 0). One endpoint is A(5, 6). Find the other coordinates of the other endpoint B.
Use the midpoint formula M[(x1 + x2)/2, (y1 + y2)/2] and let the coordinates of B be (x2, y2)
Let x1 = 5 and y1 = 6 and solve the two equations below:
(5 + x2)/2 = -1 and (6 + y2)/2 = 0
Solve (6 + y2)/2 = 0
Multiply both sides of (6 + y2)/2 = 0 by 2
2(6 + y2)/2 = 0(2)
Simplify
6 + y2 = 0
Subtract 6 from both sides of the equation
6 - 6 + y2 = 0 - 6
Simplify
y2 = -6
Solve (5 + x2)/2 = -1
Multiply both sides of (5 + x2)/2 = -1 by 2
2(5 + x2)/2 = -1(2)
Simplify
5 + x2 = -2
Subtract 5 from both sides of the equation
5 - 5 + x2 = -2 - 5
Simplify
x2 = -7
The coordinates other endpoint B are (-7, -6)