I'll solve this step by step.
First, I need to understand what the task is asking. The worksheet is titled "Distance Formula" and shows an example of how to calculate the distance between two points using the distance formula: Distance = √[(x₂-x₁)² + (y₂-y₁)²].
The example calculates the distance between points (1, 1) and (4, 5):
√[(4-1)² + (5-1)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.00 units
Now I need to solve for all the pairs of points listed in the worksheet. Let me go through each one:
1. Points (2, 3) and (7, 8)
Distance = √[(7-2)² + (8-3)²] = √[5² + 5²] = √[25 + 25] = √50 ≈ 7.07 units
2. Points (0, 0) and (6, 8)
Distance = √[(6-0)² + (8-0)²] = √[6² + 8²] = √[36 + 64] = √100 = 10.00 units
3. Points (3, -1) and (8, 4)
Distance = √[(8-3)² + (4-(-1))²] = √[5² + 5²] = √[25 + 25] = √50 ≈ 7.07 units
4. Points (-2, 5) and (3, -1)
Distance = √[(3-(-2))² + (-1-5)²] = √[5² + (-6)²] = √[25 + 36] = √61 ≈ 7.81 units
5. Points (-4, -2) and (1, 3)
Distance = √[(1-(-4))² + (3-(-2))²] = √[5² + 5²] = √[25 + 25] = √50 ≈ 7.07 units
6. Points (2, 7) and (8, 1)
Distance = √[(8-2)² + (1-7)²] = √[6² + (-6)²] = √[36 + 36] = √72 ≈ 8.49 units
7. Points (-3, 2) and (5, -4)
Distance = √[(5-(-3))² + (-4-2)²] = √[8² + (-6)²] = √[64 + 36] = √100 = 10.00 units
8. Points (1, 5) and (7, 1)
Distance = √[(7-1)² + (1-5)²] = √[6² + (-4)²] = √[36 + 16] = √52 ≈ 7.21 units
9. Points (0, 0) and (3, 4)
Distance = √[(3-0)² + (4-0)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.00 units
10. Points (-1, -1) and (4, 4)
Distance = √[(4-(-1))² + (4-(-1))²] = √[5² + 5²] = √[25 + 25] = √50 ≈ 7.07 units
The solution involves applying the distance formula to each pair of points and rounding to the nearest hundredth as instructed.
Parent Tip: Review the logic above to help your child master the concept of distance formula worksheet 1.
