Worksheets · Pre-Algebra

Distance formula worksheet for Pre-Algebra

In Pre-Algebra distance on the coordinate plane uses the Pythagorean theorem: the horizontal and vertical changes are the legs, and the segment is the hypotenuse. Some answers are whole numbers; the rest are left as simplified square roots.

Also taught in Algebra 1 and Geometry, each at its own level and with its own examples.

Not quite the one you need? Same words, different skill:

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Distance Formula

Date Period

Find each distance.

  1. Find the exact distance between two points

    Find the exact distance between (−1,−8) and (−21,13).
  2. Find the exact distance between (7,−4) and (−5,−20).
  3. Find the exact distance between (1,−4) and (8,−28).
  4. Find the exact distance between (−7,5) and (1,20).
  5. Find the exact distance between (−9,0) and (−19,−24).
  6. Find the exact distance between (4,3) and (−8,−6).
  7. Find the exact distance between (−3,−9) and (−18,−17).
  8. Find the exact distance between (0,−7) and (12,9).
  9. Find the exact distance between (−4,−9) and (3,−33).
  10. Find the exact distance between (4,7) and (24,−14).

  1. Find the distance from a graph

    Find the exact distance between A and B.−10−10−5−551010AB5
  2. Find the exact distance between A and B.−10−10−5−5551010AB
  3. Find the exact distance between A and B.−10−10−5−5551010AB
  4. Find the exact distance between A and B.−10−10−5−5551010AB
  5. Find the exact distance between A and B.−10−10−5−5551010AB
  6. Find the exact distance between A and B.−10−10−5−551010AB5
  7. Find the exact distance between A and B.−10−10−5−5551010AB
  8. Find the exact distance between A and B.−10−10−5−5551010AB
  9. Find the exact distance between A and B.−10−10−5−5551010AB
  10. Find the exact distance between A and B.−10−10−5−5551010AB

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Distance FormulaAnswer keyVersion 3

Date Period

Find each distance.

  1. Find the exact distance between two points

    Find the exact distance between (−1,−8) and (−21,13).29
  2. Find the exact distance between (7,−4) and (−5,−20).20
  3. Find the exact distance between (1,−4) and (8,−28).25
  4. Find the exact distance between (−7,5) and (1,20).17
  5. Find the exact distance between (−9,0) and (−19,−24).26
  6. Find the exact distance between (4,3) and (−8,−6).15
  7. Find the exact distance between (−3,−9) and (−18,−17).17
  8. Find the exact distance between (0,−7) and (12,9).20
  9. Find the exact distance between (−4,−9) and (3,−33).25
  10. Find the exact distance between (4,7) and (24,−14).29

  1. Find the distance from a graph

    Find the exact distance between A and B.−10−10−5−551010AB55
  2. Find the exact distance between A and B.−10−10−5−5551010AB10
  3. Find the exact distance between A and B.−10−10−5−5551010AB13
  4. Find the exact distance between A and B.−10−10−5−5551010AB13
  5. Find the exact distance between A and B.−10−10−5−5551010AB10
  6. Find the exact distance between A and B.−10−10−5−551010AB55
  7. Find the exact distance between A and B.−10−10−5−5551010AB10
  8. Find the exact distance between A and B.−10−10−5−5551010AB5
  9. Find the exact distance between A and B.−10−10−5−5551010AB13
  10. Find the exact distance between A and B.−10−10−5−5551010AB5

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Find the distance from (1,1) to (4,5)

  1. Across: 4 - 1 = 3. Up: 5 - 1 = 4.
  2. √(3² + 4²) = √25.

The answer is 5.

Where students go wrong

Adding the horizontal and vertical distances. 3 + 4 = 7 is the walk along the grid lines; the straight-line distance is the hypotenuse, 5.

Also called distance between two points or Pythagoras on a grid.

What you can put on this worksheet

The distance between two points
Find the exact distance between (4,−8) and (20,−20). → 20
Distance read off a grid
Find the exact distance between A and B. → 13
Distances, rounded
Find the distance between (6,1) and (3,4), to the nearest tenth → 4.2
Find the missing coordinate from the distance
The distance from (1,−5) to (9,y) is 10. Find every possible y → {−11,1}
Decimal coordinates, rounded
Find the distance between (0.6,1.1) and (4.4,−8.1), to the nearest tenth → 10.0
Radical coordinates
Find the distance between (5,−47) and (−65,−67) → 273

Questions about these worksheets

Yes. Every distance formula sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Pre-Algebra is usually taken around 7th or 8th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the distance formula questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 6: the distance between two points, distance read off a grid, distances, rounded, find the missing coordinate from the distance, decimal coordinates, rounded and radical coordinates. Tick as many as you want and set how many of each, or let it spread them evenly.

Forgetting to square the differences, or rounding too early. The answer is exact until you choose to round it, and simplifying the root is part of finishing.