Distance between two pointsPoints across all four quadrants
Name: Date:
Find the distance between the two points. Watch the signs.
1 units
2 units
3 units
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5 units
6 units
Distance formula worksheets
Two points anywhere on the plane make a right triangle nobody has drawn yet, and the line between them is its longest side. These free printable worksheets place the points across all four quadrants, so the legs are found by subtracting through zero.
Kid stuck on one? You don’t just get the sheet.
Distance formula
The answer key prints on a separate page.
What's on this sheet
The first-quadrant distance sheets keep both points in the top-right corner, where every gap is a plain subtraction. This one spreads the points across all four quadrants, so a leg runs from a negative coordinate to a positive one — the horizontal gap between −3 and 5 is 8, not 2 — and reading that gap correctly is the part these figures are built to train.
Why this sheet works
There is still no new theorem. The distance formula is a squared plus b squared equals c squared with the two legs written as subtractions, and a length has no sign, so the minus signs fall away the moment the gap is found. A child who has been taught the formula as a fourth thing to memorize has been given something extra to forget; the step-by-step walk says the theorem out loud instead.
How this one works
One question from this sheet, worked through a step at a time.
(0, −1) to (3, −5)
(0, −1)to(3, −5)
across=3 − 0 = 3
up=−5 − (−1) = −4
3² + 4²=25
3² + 4²=25
distance=5 units
- There is no new formula here. Draw the horizontal and vertical steps between the two points and they make a right triangle — the line you were given is its longest side.
- Across: 3 − 0 = 3, so that side is 3 long. Up: −5 − (−1) = −4, so that side is 4. A length has no sign, so take both as positive.
- Now it is the theorem you already know: 3² + 4² = 9 + 16 = 25.
- The distance is the square root of that: √25 = 5. So the two points are 5 units apart.