# 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:

$\left(\frac{{x}_{1}+{x}_{2}}{2},\frac{{y}_{1}+{y}_{2}}{2}\right)$

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.

 $\left(\frac{4+8}{2},\frac{13+5}{2}\right)$ Substitute. $\left(\frac{12}{2},\frac{18}{2}\right)$ 4 + 8 = 12 and 13 + 5 = 18 (6, 9) We can further simplify by dividing. 12/2 = 6 and 18/2 = 9.

(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.

 $\left(\frac{-3+17}{2},\frac{5+6}{2}\right)$ Substitute. $\left(\frac{14}{2},\frac{11}{2}\right)$ -3 + 17 = 14 and 5 + 6 = 11 (7, 5.5) We can further simplify by dividing. 14/2 = 7 and 11/2 = 5.5.

(7, 5.5) is the midpoint between (-3, 5) and (17, 6).