# Midpoint Formula

The midpoint formula finds the midpoint of the distance of two coordinates (x_{1}, y_{1}) and (x_{2}, y_{2}) 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 (x_{1}, y_{1}) and (x_{2}, y_{2})

Point 1: (4, 3) → X_{1} = 4, y_{1} = 13

Point 2: (8, 5) → X_{2} = 8, y_{2} = 5

Step 2:

Substitute into formula and simplify.

$(\frac{4+8}{2},\frac{13+5}{2})$ | Substitute. |

$(\frac{12}{2},\frac{18}{2})$ | 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 (x_{1}, y_{1}) and (x_{2}, y_{2})

Point 1: (-3, 5) → X_{1} = -3, y_{1} = 5

Point 2: (17, 6) → X_{2} = 17, y_{2} = 6

Step 2:

Substitute into formula and simplify.

$(\frac{-3+17}{2},\frac{5+6}{2})$ | Substitute. |

$(\frac{14}{2},\frac{11}{2})$ | -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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