Question

Apply the Pythagorean Theorem to find the length between (2,7) and (−2, 0) . Round your answer to the nearest hundredth, if necessary. Show your work.(1 point) Responses 5.74 5 point 7 4 11 11 8.06 8 point 0 6 65 65

Answer 1

To find the length between the points (2, 7) and (−2, 0), we can use the Pythagorean Theorem.

1. **Identify the coordinates**:
- Point A: (2, 7)
- Point B: (−2, 0)

2. **Calculate the differences in the x and y coordinates**:
- \( \Delta x = x_2 - x_1 = -2 - 2 = -4 \)
- \( \Delta y = y_2 - y_1 = 0 - 7 = -7 \)

3. **Use the Pythagorean Theorem**:
The distance \( d \) between two points in a plane can be calculated using the formula:
\[
d = \sqrt{(\Delta x)^2 + (\Delta y)^2}
\]

Plug in the values we calculated:
\[
d = \sqrt{(-4)^2 + (-7)^2}
\]

4. **Calculate the squares**:
\[
d = \sqrt{16 + 49}
\]

5. **Add the squares**:
\[
d = \sqrt{65}
\]

6. **Calculate the square root**:
Using a calculator,
\[
d \approx 8.06
\]

Thus, the length between the points (2, 7) and (−2, 0) is approximately **8.06**.

Final answer: **8.06**