Midpoint Formula
The midpoint formula finds the midpoint of the distance of two coordinates (x1, y1) and (x2, y2) on the Cartesian plane.
The midpoint formula:
The formula is in the form of an ordered pair because the answer is an ordered pair.
Example 1:
Find the midpoint between (4, 13) and (8, 5).
Step 1:
Assign coordinate values to (x1, y1) and (x2, y2)
Point 1: (4, 3) → X1 = 4, y1 = 13
Point 2: (8, 5) → X2 = 8, y2 = 5
Step 2:
Substitute into formula and simplify.
| Substitute. | |
| 4 + 8 = 12 and 13 + 5 = 18 | |
| (6, 9) | We can further simplify by dividing. 12/2 = 6 and 18/2 = 9. |
Answer:
(6, 9) is the midpoint between (4, 13) and (8, 5).
Example 2:
Find the midpoint between (-3, 5) and (17, 6).
Step 1:
Assign coordinate values to (x1, y1) and (x2, y2)
Point 1: (-3, 5) → X1 = -3, y1 = 5
Point 2: (17, 6) → X2 = 17, y2 = 6
Step 2:
Substitute into formula and simplify.
| Substitute. | |
| -3 + 17 = 14 and 5 + 6 = 11 | |
| (7, 5.5) | We can further simplify by dividing. 14/2 = 7 and 11/2 = 5.5. |
Answer:
(7, 5.5) is the midpoint between (-3, 5) and (17, 6).
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