# Distance Formula

The distance formula to find the distance between two points (x1, y1) and (x2, y2) is derived from the Pythagorean Theorem.

Let A and B be two points on the coordinate plane, with coordinates (x1, y1) and (x2, y2) respectively. See the figure below: Then by Pythagorean Theorem, AB2  Example: Find the distance between the points (8, -4) and (8, -7).

Let us assume (x1, y1) = (8, -4) and (x2, y2) = (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 (x1, y1) = (-6, -1) and (x2, y2) = (2, 5)

Then distance between the given points = = =  = = = 10 units Find the distance between each pair of points.

1. (-2, -2), (-5, -6)
2. (-4, 0), (-7, 0)
3. (-1, 6), (7, 0)
4. (2, -3), (3, -5)
5. (-8, 1), (7, 1)
1. 5 units
2. 3 units
3. 10 units
4. units
5. 15 units

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