Midpoint of a line segment
To find the midpoint of a line segment on the coordinate system, simply take the average of the x-coordinates and the
average of the y-coordinates.
Let (x
1 , y
1) and (x
2 , y
2) represent the endpoints of a line segment.
Therefore, the formula to get the midpoint is: [(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2]
A couple of examples showing how to find the midpoint of a line segment
Example #1:
Graph (2, 4) and (4, 8) and find the midpoint
[(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2] = [(2 + 4) ÷ 2, (4 + 8)÷ 2]
[(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2] = (6 ÷ 2, 12 ÷ 2)
[(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2] = (3, 6)
The graph is shown below.
Example #2:
Graph (-4, 2) and (0, 6) and find the midpoint.
[(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2] = [(-4 + 0) ÷ 2, (2 + 6)÷ 2]
[(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2] = (-4 ÷ 2, 8 ÷ 2)
[(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2] = (-2, 4)
The graph is shown below:
Example #3:
Using (5, -5) and (-1, 1), find the midpoint.
[(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2] = [(5 + -1) ÷ 2, (-5 + 1)÷ 2]
[(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2] = (4 ÷ 2, -4 ÷ 2)
[(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2] = (2, -2)
Example #4:
Using (12, 0) and (-12, 2), find the midpoint.
[(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2] = [(12 + -12) ÷ 2, (0 + 2)÷ 2]
[(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2] = (0 ÷ 2, 2 ÷ 2)
[(x
1 + x
2) ÷ 2 , (y
1 + y
2) ÷ 2] = (0, 1)
-
May 26, 22 06:50 AM
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