# Distance Formula

## Grade 8 Math Worksheets

The distance formula to find the distance between two points (*x*_{1}, *y*_{1}) and (*x*_{2}, *y*_{2}) is derived from the Pythagorean Theorem.

Let *A* and *B* be two points on the coordinate plane, with coordinates (*x*_{1}, *y*_{1}) and (*x*_{2}, *y*_{2}) respectively. See the figure below:

Then by Pythagorean Theorem, *AB*^{2} =

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*Example:***Find the distance between the points (8, -4) and (8, -7).**

Let us assume (*x*_{1}, *y*_{1}) = (8, -4) and (*x*_{2}, *y*_{2}) = (8, -7)

Then distance between the given points =

= = = = **3 units**

* *

*Example:***What is the distance between the points (-6, -1) and (2, 5)?**

Let us assume (*x*_{1}, *y*_{1}) = (-6, -1) and (*x*_{2}, *y*_{2}) = (2, 5)

Then distance between the given points =

= =

= = = = **10 units**

**Check Point**

Find the distance between each pair of points.

- (-2, -2), (-5, -6)
- (-4, 0), (-7, 0)
- (-1, 6), (7, 0)
- (2, -3), (3, -5)
- (-8, 1), (7, 1)

##### Answer key

- 5 units
- 3 units
- 10 units
- units
- 15 units

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