Distance Formula Answer Key
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Distance Formula Answer Key
📏 Part 1: Basic Distance Calculations
Answer: 6 units (|8 - 2| = 6)
Answer: 6 units (|7 - 1| = 6)
Answer: 5 units
Work:
Horizontal distance: |4 - 1| = 3
Vertical distance: |6 - 2| = 4
Distance = √(3² + 4²) = √(9 + 16) = √25 = 5
Answer: √34 ≈ 5.83 units
Work:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(3 - (-2))² + (-2 - 1)²]
d = √[(5)² + (-3)²] = √[25 + 9] = √34
📐 Part 2: Distance Formula Applications
Answer: d = √(a² + b²)
Answer: 5 units
Work:
d = √[(2 - (-1))² + (1 - (-3))²]
d = √[(3)² + (4)²] = √[9 + 16] = √25 = 5
Answer: 10 units
Work:
d = √[(6 - 0)² + (8 - 0)²]
d = √[36 + 64] = √100 = 10
🎯 Part 3: Creative & Blended Learning Components
Answer: Answers will vary based on student creativity. Check that:
• Problem includes two coordinate points
• Calculation is shown correctly using distance formula
• Final answer is simplified or rounded appropriately
Answer: Answers will vary. Students should demonstrate:
• Correct plotting of points on digital graphing tool
• Screenshot or description of verification process
• Comparison between calculated and digital tool results
Sample Answer: Answers will vary. Example:
"A football player runs from the 20-yard line at the left sideline to the 35-yard line at the right sideline. Using coordinates (0, 20) and (53, 35), the distance is √[(53-0)² + (35-20)²] = √[2809 + 225] = √3034 ≈ 55.1 yards."
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