## Lesson

##### Distance formula

#### [Formula]

## Example

Show that the distance between the two points (8,6) and (4,2) is the same as the distance between the two points (9,4) and (13, 0).

## Solution

Recall the distance formula

Let x_{1} = 8, x_{2} = 4, y_{1} = 6, y_{2} = 2

Repeating the process:

Let x_{1} = 9, x_{2} = 13, y_{1} = 4, y_{2} = 0

Therefore:

d_{1} = d_{2}

and so the distance between the two sets of points are equal

## Question

Determine the distance between the points (-5,-7) and (-3,1), simplifying your answer where necessary

## Explanation

The distance between 2 points (x_{1}, y_{1}) and (x_{2,} y_{2}) is found using the formula

When applied to the points (-5,-7) and (-3,1), we have

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