Distance Formula Explained

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📚 Understanding the Distance Formula

The Distance Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]

This formula helps us find the distance between two points on a coordinate plane.

1. What does the distance formula calculate?

The slope of a line

The distance between two points

The area of a triangle

The midpoint of a line

2. In the formula d = √[(x₂ - x₁)² + (y₂ - y₁)²], what do x₁ and y₁ represent?

The coordinates of the second point

The coordinates of the first point

The distance values

The slope values

3. Why do we square the differences (x₂ - x₁) and (y₂ - y₁)?

To make the numbers bigger

To eliminate negative values

To find the area

To make calculations easier

✏️ Step-by-Step Practice

4. Find the distance between points A(3, 4) and B(6, 8). Show your work:

Step 1: Identify the coordinates: (x₁, y₁) = (_____, _____) and (x₂, y₂) = (_____, _____)

Step 2: Find x₂ - x₁ = _____ - _____ = _____

Step 3: Find y₂ - y₁ = _____ - _____ = _____

Step 4: Square both differences: (_____)² = _____ and (_____)² = _____

Step 5: Add the squares: _____ + _____ = _____

Step 6: Take the square root: √_____ = _____

5. Calculate the distance between points C(1, 2) and D(4, 6):

6. Explain in your own words why we use the Pythagorean theorem in the distance formula:

🎯 Real-World Application

7. A park has two playgrounds. Playground A is at coordinates (2, 3) and Playground B is at coordinates (8, 11). If each unit represents 50 metres, what is the actual distance between the playgrounds?

Distance formula calculation:

Convert to metres: _____ units × 50 metres/unit = _____ metres

8. True or False: The distance formula will always give a positive answer.

True

False

Explain your reasoning:

Distance Formula Explained

Distance Formula Explained

📚 Understanding the Distance Formula

✏️ Step-by-Step Practice

🎯 Real-World Application

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