Distance between two pointsPoints in the first quadrant
Name: Date:
Find the distance between the two points.
1 units
2 units
3 units
4 units
5 units
6 units
Distance between two points worksheets
There is no new theorem on these sheets — only a new place to notice the old one. Two points on a grid make a right triangle nobody has drawn yet, and the line between them is its longest side.
Kid stuck on one? You don’t just get the sheet.
Distance between two points
The answer key prints on a separate page.
What's on this sheet
The figure shows the two points and the line joining them, and deliberately nothing else. Seeing that the horizontal and vertical gaps form a right triangle IS this standard; a picture that draws those two sides in has answered its own question and left an arithmetic exercise behind. The step-by-step walk adds them one at a time, which is where they belong.
Why this sheet works
That also means the distance formula does not need to be memorized as a fourth thing. It is a² + b² = c² with the two legs written as subtractions, and a child who has been taught it as its own formula has been given something extra to forget. Every walk here says the theorem out loud rather than quoting the formula.
How this one works
One question from this sheet, worked through a step at a time.
(4, 7) to (8, 10)
(4, 7)to(8, 10)
across=8 − 4 = 4
up=10 − 7 = 3
4² + 3²=25
4² + 3²=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: 8 − 4 = 4, so that side is 4 long. Up: 10 − 7 = 3, so that side is 3. A length has no sign, so take both as positive.
- Now it is the theorem you already know: 4² + 3² = 16 + 9 = 25.
- The distance is the square root of that: √25 = 5. So the two points are 5 units apart.