Midpoint Formula

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:

(x1+x22,y1+y22)

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.

(4+82,13+52)Substitute.
(122,182)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.

(-3+172,5+62)Substitute.
(142,112)-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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