Question

Use the image to answer the 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.