# Distance Formula

See how to use the distance formula

to find the distance between two points (2D, 3D).

2 examples and their solutions.

## Distance Formula (2D)

### Formula

d = √(x

_{2}- x

_{1})

^{2}+ (y

_{2}- y

_{1})

^{2}

### Example

Distance between (-3, 1) and (5, 4)

Solution (-3, 1), (5, 4)

d = √(5 - (-3))

= √(5 + 3)

= √8

= √64 + 9

= √73

d = √(5 - (-3))

^{2}+ (4 - 1)^{2}= √(5 + 3)

^{2}+ 3^{2}= √8

^{2}+ 3^{2}= √64 + 9

= √73

Close

## Distance Formula (3D)

### Formula

d = √(x

_{2}- x

_{1})

^{2}+ (y

_{2}- y

_{1})

^{2}+ (z

_{2}- z

_{1})

^{2}

### Example

Distance between (2, -1, 3) and (5, 0, 1)

Solution (2, -1, 3), (5, 0, 1)

d = √(5 - 2)

= √3

= √9 + 1 + 4

= √10 + 4

= √14

d = √(5 - 2)

^{2}+ (0 - (-1))^{2}+ (1 - 3)^{2}= √3

^{2}+ (-1)^{2}+ (-2)^{2}= √9 + 1 + 4

= √10 + 4

= √14

Close