Distance Between Two Points Worksheets
Free printable distance between two points worksheets: use the Pythagorean theorem on a four-quadrant grid, to the nearest tenth, with an answer key.
Each grid shows six lettered points, and four questions beside it ask how far apart two of them are. No pair lies along a gridline, so every distance is the long side of a right triangle: count the legs across and up, square them, add, and take the square root. From (-2, 3) to (3, 5) that is 5² + 2² = 29, about 5.4 units.
On every grid two of the four distances come out whole - 5 or 10 units, from legs of 3 and 4 or 6 and 8 - and two are rounded to the nearest tenth. Every question asks for the nearest tenth, so the wording gives nothing away. The points sit on grid crossings from -5 to 5, never on an axis, and the answer key shows the sum of the squares before the distance.
What this worksheet covers
- Find the distance between two points with the Pythagorean theorem
- Round a distance to the nearest tenth
Common Core standards
- 8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Frequently asked questions
How do you find the distance between two points on a grid?
Make a right triangle: go straight across from one point and straight up or down to the other. Count the two legs, square them, add, and take the square root. From (-2, 3) to (3, 5) the legs are 5 and 2, so 25 + 4 = 29, and the distance is about 5.4 units.
Why round to the nearest tenth?
Because most distances on a grid are not whole numbers: 29 is not a square number, so its square root never ends. Only some pairs give a whole answer, such as legs of 3 and 4, which give 5. Every question asks for the nearest tenth anyway, so the wording does not give away which ones come out whole.
What does the answer key show?
The two legs squared and added, then the distance: 3² + 4² = 25: 5 units, or 5² + 2² = 29: about 5.4 units. When an answer is wrong, the sum shows whether the legs were counted wrongly or the square root was.
What grade is finding the distance between two points?
Eighth grade. It is the Pythagorean theorem used on a coordinate grid, so a student should be at ease with right triangles first; the Pythagorean theorem worksheets come before it.