Distance Between Two Points | Worksheet - Free Printable

To find the distance between two points on a coordinate grid, we can use the Pythagorean theorem. This means:

1. Find how far apart the points are horizontally (left-right).
2. Find how far apart they are vertically (up-down).
3. Treat those as the legs of a right triangle.
4. Use the formula:
distance = √(horizontal² + vertical²)

Let’s solve each pair one by one.

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First Pair: Point X and Point Y

- Point X is at (-5, 6)
- Point Y is at (-7, -3)

Horizontal distance = |−5 − (−7)| = |−5 + 7| = 2
Vertical distance = |6 − (−3)| = |6 + 3| = 9

Now plug into the formula:
Distance = √(2² + 9²) = √(4 + 81) = √85 ≈ 9.22 units

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Second Pair: Point M and Point N

- Point M is at (-8, -4)
- Point N is at (6, 0)

Horizontal distance = |−8 − 6| = |−14| = 14
Vertical distance = |−4 − 0| = 4

Distance = √(14² + 4²) = √(196 + 16) = √212 ≈ 14.56 units

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Third Pair: Point A and Point B

- Point A is at (-3, 7)
- Point B is at (4, -5)

Horizontal distance = |−3 − 4| = 7
Vertical distance = |7 − (−5)| = 12

Distance = √(7² + 12²) = √(49 + 144) = √193 ≈ 13.89 units

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Fourth Pair: Point O and Point P

- Point O is at (-5, 8)
- Point P is at (5, -6)

Horizontal distance = |−5 − 5| = 10
Vertical distance = |8 − (−6)| = 14

Distance = √(10² + 14²) = √(100 + 196) = √296 ≈ 17.20 units

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Final Answer:
9.22, 14.56, 13.89, 17.20