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Pythagorean theorem practice

Distance between two points worksheets

Find distances on four coordinate grids with whole-number, decimal-tenths, radical or mixed coordinates. Choose first-quadrant or four-quadrant points and print separate worked solutions.

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Read the coordinates of P1 and P2, then find their distance. Show the coordinate differences and squared sum. Round noninteger answers to four decimal places.

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A4

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Turn coordinate differences into a right triangle

The first-quadrant setting uses nonnegative coordinates. Four-quadrant practice adds negative coordinates, so learners must track the signs in each subtraction. Each worksheet contains four pairs of points on separate grids.

Keep the squared calculations exact until the final step. The worked key distinguishes an exact answer from an approximation and rounds noninteger roots to four decimal places. Length and distance are always nonnegative.

Learning objective

What this activity builds

Interpret coordinate differences as the horizontal and vertical legs of a right triangle and calculate a nonnegative distance.

Worked example

Find the distance from (−2, 1) to (1, 5).

5 units.

The horizontal difference is 1 − (−2) = 3 and the vertical difference is 5 − 1 = 4. The squared distance is 3² + 4² = 25, so the distance is 5. Reversing the points changes the signs of the differences but not their squares.

Teaching notes

Make the practice count

  • Draw horizontal and vertical helper legs before applying the formula.
  • Keep x differences together and y differences together.
  • Put a negative coordinate in parentheses when substituting it into a subtraction.
  • Use whole numbers first, then choose tenths or radicals; mixed sheets include all three coordinate types.
  • Keep exact coordinate values through the squared sum and round only the final distance.
  • Check a horizontal or vertical pair by counting grid units directly.

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Customize the practice

Choose your options, update the preview, then download the exact same pages.

Choose whole-number, decimal-tenths, radical or mixed coordinates. Mixed sheets include all three types. Use the exact coordinates printed beside each grid and round only the final distance when needed.

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Math SheetNameScore/ 4TeacherDateDistance Between PointsFind the distance between each pair of points. Distances are always nonnegative.1.-5-5-4-4-2-200224455P1P2P1 (-1, 1)P2 (-3, -1)Work:2.-5-5-4-4-2-200224455P1P2P1 (3, -1)P2 (-1, 5)Work:3.-5-5-4-4-2-200224455P1P2P1 (5, -1)P2 (5, 3)Work:4.-5-5-4-4-2-200224455P1P2P1 (1, -1)P2 (3, 4)Work:math-sheet.comPage 1 / 1

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