### Distance Formula in the Coordinate Plane

The distance between two points and can be defined as . This is called the **distance formula**. Remember that distances are always positive!

What if you were given the coordinates of two points? How could you find how far apart these two points are?

### Examples

#### Example 1

Find the distance between (-2, -3) and (3, 9).

Use the distance formula, plug in the points, and simplify.

#### Example 2

Find the distance between (12, 26) and (8, 7).

Use the distance formula, plug in the points, and simplify.

#### Example 3

Find the distance between (4, -2) and (-10, 3).

Plug in (4, -2) for and (-10, 3) for and simplify.

#### Example 4

Find the distance between (3, 4) and (-1, 3).

Plug in (3, 4) for and (-1, 3) for and simplify.

#### Example 5

Find the distance between (4, 23) and (8, 14).

Plug in (4, 23) for and (8, 14) for and simplify.

### Review

Find the distance between each pair of points. Round your answer to the nearest hundredth.

- (4, 15) and (-2, -1)
- (-6, 1) and (9, -11)
- (0, 12) and (-3, 8)
- (-8, 19) and (3, 5)
- (3, -25) and (-10, -7)
- (-1, 2) and (8, -9)
- (5, -2) and (1, 3)
- (-30, 6) and (-23, 0)
- (2, -2) and (2, 5)
- (-9, -4) and (1, -1)

### Review (Answers)

To see the Review answers, open this PDF file and look for section 3.10.

### Resources