Quiz and worksheet on using the distance formula, with questions and answer options.

I'll solve each problem step by step, working through the calculations carefully.

Problem 1: Which is the distance formula?

The distance formula calculates the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane. It's derived from the Pythagorean theorem and is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Looking at the options, the first choice matches this formula exactly.

Problem 2: Find the distance between (4, 1) and (10, 9)

Let me calculate this carefully:
- Point 1: (x₁, y₁) = (4, 1)
- Point 2: (x₂, y₂) = (10, 9)

Using the distance formula:
d = √[(10 - 4)² + (9 - 1)²]
d = √[6² + 8²]
d = [36 + 64]
d = √100
d = 10

Let me verify: 6² = 36, 8² = 64, 36 + 64 = 100, √100 = 10 ✓

Problem 3: Find the distance between (-3, 4) and (2, 5)

Let me calculate this carefully:
- Point 1: (x₁, y₁) = (-3, 4)
- Point 2: (x₂, y₂) = (2, 5)

Using the distance formula:
d = √[(2 - (-3))² + (5 - 4)²]
d = √[(2 + 3)² + 1²]
d = √[5² + 1²]
d = √[25 + 1]
d = √26

Let me verify: 2 - (-3) = 2 + 3 = 5, 5² = 25, 5 - 4 = 1, 1² = 1, 25 + 1 = 26, so d = √26 ✓

Final Answer:
1. d = √[(x₂ - x₁)² + (y₂ - y₁)²]
2. 10
3. 26