Midpoint of a line segment
To find the midpoint of a line segment on the coordinate system, simply take the average of the xcoordinates and the
average of the ycoordinates.
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)

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