Distance Formula Practice- Worksheet with Answers

What This Worksheet Actually Is

You're here because you need practice problems for the distance formula. Not explanations. Not theory. Practice problems with answers so you can check your work and actually learn something.

This worksheet gives you 15 problems ranging from basic to intermediate. The answers are included at the end. No excuses for not knowing if you're wrong.

The Distance Formula Basics

If you forgot how this works, here's the reminder:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

You find the difference between x-coordinates, square it. Find the difference between y-coordinates, square it. Add them together. Take the square root.

That's it. No tricks.

Distance Formula Practice Problems

Set 1: Basic Level

Find the distance between each pair of points.

Problem 1: (0, 0) and (3, 4)

Problem 2: (1, 2) and (4, 6)

Problem 3: (-2, 3) and (2, 6)

Problem 4: (5, 1) and (1, 5)

Problem 5: (-3, -4) and (0, 0)

Set 2: Intermediate Level

Calculate the distance. Watch the signs.

Problem 6: (-1, -1) and (3, 4)

Problem 7: (2, -3) and (-4, 1)

Problem 8: (-5, 2) and (1, -2)

Problem 9: (7, 8) and (3, 5)

Problem 10: (-2, 5) and (4, -1)

Set 3: Application Problems

These require you to set up the points first.

Problem 11: A rectangle has vertices at (0, 0), (6, 0), (6, 4), and (0, 4). Find the perimeter.

Problem 12: Point A is at (1, 3), Point B is at (4, 7). Point C is at (7, 3). Is triangle ABC isosceles?

Problem 13: Two cities are located at (2, 5) and (10, 12) on a coordinate map where 1 unit = 50 miles. What's the actual distance?

Problem 14: Find the length of the diagonal of a square with vertices at (2, 2), (2, 6), (6, 6), and (6, 2).

Problem 15: A triangle has sides measuring 5, 12, and 13 units. Is it a right triangle? Hint: Check if the Pythagorean theorem works.

Answers

Problem	Answer	Quick Check
1	5	3-4-5 triangle
2	5	√25
3	5	√25
4	√32 ≈ 5.66	4√2
5	5	3-4-5 triangle
6	√41 ≈ 6.40	Negative to positive
7	√52 ≈ 7.21	2√13
8	√52 ≈ 7.21	2√13
9	5	√25
10	√72 ≈ 8.49	6√2

Problem	Answer	Explanation
11	20 units	Two sides: 6 units, Two sides: 4 units. Perimeter = 2(6) + 2(4) = 20
12	Yes	AB = √32, BC = √32. Equal sides = isosceles
13	≈ 480.8 miles	Distance ≈ √125, times 50 miles/unit
14	√32 ≈ 5.66	Diagonal of 4×4 square
15	Yes	5² + 12² = 25 + 144 = 169 = 13² ✓

Common Mistakes to Avoid

Forgetting to square the differences — You must square before adding. Skipping this step gives you garbage.
Forgetting to take the square root — The formula gives you the sum under the radical. You still need to finish.
Sign errors on negative coordinates — Subtracting a negative is addition. Don't panic when you see double negatives.
Rounding too early — Keep the exact form (√50) until the final answer unless told otherwise.

How to Use This Worksheet

Don't just read through the answers. That's useless.

Solve each problem on paper first. Show your work.
Check your answer against the answer key.
If you're wrong, find where you messed up. Arithmetic error? Formula setup error?
Redo the problem without looking at the solution.
Move on when you can solve it consistently.

If you get more than 3 wrong, go back and review the formula. There's no shame in that. But don't just copy answers and call it practice.

When You're Done

If you can solve all 15 problems correctly, you understand the distance formula. If you can't, identify which ones gave you trouble and practice those specific types.

That's the entire worksheet. Use it properly.