What if you were given the coordinates of two points? How could you find how far apart these two points are? After completing this Concept, you'll be able to find the distance between two points in the coordinate plane using the Distance Formula.

### Watch This

CK-12 Finding The Distance Between Two Points

James Sousa: The Distance Formula

### Guidance

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

#### Example A

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

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

#### Example B

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

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

#### Example C

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

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

CK-12 Finding The Distance Between Two Points

### Guided Practice

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

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

3. Find the distance between (5, 2) and (6, 1)

**Answers**

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

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

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

### Practice

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)