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[(x_{1} + x_{2})/2, (y_{1} + y_{2})/2] and let the coordinates of B be (x_{2}, y_{2})
Notice that (x_{1} + x_{2})/2 is the x-coordinate of the midpoint. So (x_{1} + x_{2})/2 = 2
Notice that (y_{1} + y_{2})/2 is the y-coordinate of the midpoint. So (y_{1} + y_{2})/2 = 3
Let x_{1} = -2 and y_{1} = -1 and solve the two equations below:
(-2 + x_{2})/2 = 2 and (-1 + y_{2})/2 = 3
Solve (-1 + y_{2})/2 = 3
Multiply both sides of (-1 + y_{2})/2 = 3 by 2
2(-1 + y_{2})/2 = 3(2)
Simplify
-1 + y_{2} = 6
Add 1 to both sides of the equation
-1 + 1 + y_{2} = 6 + 1
Simplify
y_{2} = 7
Solve (-2 + x_{2})/2 = 2
Multiply both sides of (-2 + x_{2})/2 = 2 by 2
2(-2 + x_{2})/2 = 2(2)
Simplify
-2 + x_{2} = 4
Add 2 to both sides of the equation
-2 + 2 + x_{2} = 4 + 2
Simplify
x_{2} = 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[(x_{1} + x_{2})/2, (y_{1} + y_{2})/2] and let the coordinates of B be (x_{2}, y_{2})
Let x_{1} = 5 and y_{1} = 6 and solve the two equations below:
(5 + x_{2})/2 = -1 and (6 + y_{2})/2 = 0
Solve (6 + y_{2})/2 = 0
Multiply both sides of (6 + y_{2})/2 = 0 by 2
2(6 + y_{2})/2 = 0(2)
Simplify
6 + y_{2} = 0
Subtract 6 from both sides of the equation
6 - 6 + y_{2} = 0 - 6
Simplify
y_{2} = -6
Solve (5 + x_{2})/2 = -1
Multiply both sides of (5 + x_{2})/2 = -1 by 2
2(5 + x_{2})/2 = -1(2)
Simplify
5 + x_{2} = -2
Subtract 5 from both sides of the equation
5 - 5 + x_{2} = -2 - 5
Simplify
x_{2} = -7
The coordinates other endpoint B are (-7, -6)
Sep 27, 22 08:34 AM