Distance & Midpoint · Grades 10–10

Distance & Midpoint Formula Worksheets

Midpoint is just the average of the coordinates; distance is Pythagoras in disguise. Worksheets for both formulas, with distances that come out as whole numbers.

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What it is

The midpoint of two points is the average of their coordinates; the distance between them uses the Pythagorean theorem on the horizontal and vertical gaps.

Why it matters

Distance and midpoint are core coordinate-geometry tools, underpinning circles, segments, and later work in geometry and physics.

How to do it

  1. Midpoint: average the x-coordinates and average the y-coordinates.
  2. Distance: find the differences in x and y.
  3. Square the differences, add, and take the square root.

Examples by level

  • BeginnerMidpoint of (1, -6) and (-1, 4) =(0, -1)
  • IntermediateDistance between (-9, 0) and (-6, 4) =5
  • AdvancedDistance between (-12, -4) and (-3, 8) =15

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

  • Adding instead of subtracting the coordinates.
  • Forgetting to square the differences in the distance formula.
  • Averaging only the x-coordinates for the midpoint.

Tips

  • Midpoint averages; distance uses the Pythagorean theorem.
  • Sketch the right triangle between the points to see why.

For parents

Midpoint is the average of the coordinates; distance uses the Pythagorean theorem on the horizontal and vertical gaps.

For teachers

Sketching the right triangle between the two points makes the distance formula feel like the Pythagorean theorem it is.

Key vocabulary

midpoint
the point halfway between two points
distance formula
√((x₂−x₁)² + (y₂−y₁)²)

Frequently asked questions

What is the distance formula?
The distance between (x₁, y₁) and (x₂, y₂) is √((x₂ − x₁)² + (y₂ − y₁)²).
What is the midpoint formula?
The midpoint is ((x₁ + x₂)/2, (y₁ + y₂)/2), the average of the coordinates.

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