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)Responses111165658.068 point 0 65.74

Answer 1

To find the distance between the points \((2, 7)\) and \((-2, 0)\) using the Pythagorean Theorem, we can use the distance formula, which is derived from the theorem.

The distance formula is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, let \((x_1, y_1) = (2, 7)\) and \((x_2, y_2) = (-2, 0)\).

Now, we can substitute these values into the formula:

1. Calculate \(x_2 - x_1\):
\[
-2 - 2 = -4
\]

2. Calculate \(y_2 - y_1\):
\[
0 - 7 = -7
\]

3. Substitute these into the distance formula:
\[
d = \sqrt{(-4)^2 + (-7)^2}
\]

4. Calculate \((-4)^2\) and \((-7)^2\):
\[
(-4)^2 = 16 \quad \text{and} \quad (-7)^2 = 49
\]

5. Add these values:
\[
16 + 49 = 65
\]

6. Take the square root:
\[
d = \sqrt{65}
\]

7. Now, we can approximate \(\sqrt{65}\):
\[
\sqrt{65} \approx 8.0623
\]

Rounding to the nearest hundredth, we have:
\[
d \approx 8.06
\]

The length between the points \((2, 7)\) and \((-2, 0)\) is approximately \(8.06\).

Based on your provided responses, it appears there may have been an error in your listed choices. The correct length is \(8.06\).