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Question

A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 9.

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.

where the points are at 3,2 and 7,8

Answer 1

To find the length between the two points (3, 2) and (7, 8) using the Pythagorean Theorem, we can follow these steps:

1. Identify the coordinates of the points:

   • Point A: (3, 2)
   • Point B: (7, 8)

2. Calculate the differences in the x-coordinates and y-coordinates:

   • Difference in x (Δx) = x₂ - x₁ = 7 - 3 = 4
   • Difference in y (Δy) = y₂ - y₁ = 8 - 2 = 6

3. Apply the Pythagorean Theorem: The length (d) between the two points can be calculated using the formula: \[ d = \sqrt{(\Delta x)^2 + (\Delta y)^2} \]

   Substituting the values we calculated: \[ d = \sqrt{(4)^2 + (6)^2} \] \[ d = \sqrt{16 + 36} \] \[ d = \sqrt{52} \]

4. Calculate the square root of 52: \[ \sqrt{52} \approx 7.2111 \]

5. Round the result to the nearest hundredth: \[ d \approx 7.21 \]

The length between the two points (3, 2) and (7, 8) is approximately 7.21.