### Midpoint Formula

You may be asked to calculate the midpoints of two points on a line on a two-dimensional graph.

In order to do so, you would take two points from the line and use the formulas provided below to find the midpoints.

midpoint *x* = (*x*_{1} + *x*_{2}) ÷ 2

midpoint *y* = (*y*_{1} + *y*_{2}) ÷ 2

### Midpoints – Practical Problems

However, you may also need to use the midpoint formula in practical problems, like the one that follows.

This is an example of a practical application of the midpoint formula, which will help you with coordinate geometry problems on the exam.

**Problem:**

Consider two stores in a town. The first store is a grocery store. The second is a pizza place where customers collect their pizzas after they order pizza online.

The grocery store is represented by the coordinates (−4, 2) and the pizza place is represented by the coordinates (2,−4).

If the grocery store and the pizza place are connected by a line segment, what is the midpoint of this line?

A. (1, 1)

B. (−1, −1)

C. (2, 2)

D. (−2, −2)

E. (−3, −3)

**The correct answer is B.**

Remember that in order to calculate midpoints, you need to use these formulas:

midpoint *x* = (*x*_{1} + *x*_{2}) ÷ 2

midpoint *y* = (*y*_{1} + *y*_{2}) ÷ 2

First, find the midpoint of the *x* coordinate:

midpoint *x* = (*x*_{1} + *x*_{2}) ÷ 2

midpoint *x* = (−4 + 2) ÷ 2

midpoint *x* = −2 ÷ 2

midpoint *x* = −1

Then find the midpoint of the *y* coordinate:

midpoint *y* = (*y*_{1} + *y*_{2}) ÷ 2

midpoint *y* = (2 + −4) ÷ 2

midpoint *y* = −2 ÷ 2

midpoint *y* = −1

So, the midpoint is (−1, −1)

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