Question

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary. (1 point) Responses 5.57 5.57 6:40 6:40 9 9 41

Answer 1

4,2.
-1, -2

Answer 2

To find the length between two points using the Pythagorean theorem, we use the formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points.

If you provide the coordinates of the two points, I can compute the length for you.

Answer 3

To find the distance between the points \( (4, 2) \) and \( (-1, -2) \), we can apply the Pythagorean Theorem as follows:

1. Identify the coordinates:
- \( (x_1, y_1) = (4, 2) \)
- \( (x_2, y_2) = (-1, -2) \)

2. Substitute the values into the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

3. Plug in the values:

\[
d = \sqrt{((-1) - 4)^2 + ((-2) - 2)^2}
\]

4. Calculate the differences:

\[
d = \sqrt{(-5)^2 + (-4)^2}
\]

5. Square the differences:

\[
d = \sqrt{25 + 16}
\]

6. Add the squares:

\[
d = \sqrt{41}
\]

7. Finally, calculate the square root:

\[
d \approx 6.4
\]

When rounded to the nearest hundredth, the distance \( d \) is approximately **6.40**.