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Distance Formula Practice

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Distance Formula Practice

Coordinate plane with distance formula illustration

📐 Part 1: Building to the Distance Formula

1. Find the length of the horizontal and vertical sides of the right triangle formed by points A(2, 3) and B(6, 7).

Horizontal distance: |6 - 2| = _______

Vertical distance: |7 - 3| = _______

2. Using the Pythagorean Theorem (a² + b² = c²), find the distance between A(2, 3) and B(6, 7).
3. Calculate the distance between each pair of points using the distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²]

a) C(1, 4) and D(5, 1)

b) E(-2, 3) and F(4, -1)

4. Challenge: Point G is at (0, 0) and point H is at (a, b). Write the distance formula for these points in terms of a and b.

💻 Part 2: Blended Learning Verification

5. Use an online graphing tool (like Desmos or GeoGebra) to plot the points from question 3 and verify your distance calculations. Record your findings:

Website used: ________________________

Distance for C(1, 4) and D(5, 1): My calculation _______ Tool result _______

Distance for E(-2, 3) and F(4, -1): My calculation _______ Tool result _______

6. Real-world application: A drone flies from the park at coordinates (2, 5) to the school at (8, 13). If each unit represents 100 feet, what is the actual distance the drone travels?

Distance in coordinate units: _______

Actual distance in feet: _______

🎨 Part 3: Create Your Own Challenge

7. Design a coordinate plane problem for your classmates! Create two points and write a story problem that requires finding the distance between them.

Point 1: ( _____ , _____ )

Point 2: ( _____ , _____ )

Your story problem:

8. Solve your own problem and show your work:

Final answer: _______

9. Reflection: How is the distance formula related to the Pythagorean Theorem? Explain in 2-3 sentences.
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