Question

Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) . Round your answer to the nearest hundredth, if necessary.(1 point) Responses 29 29 5.39 5.39 4.58 4.58 2.65

Answer 1

To find the distance between the points \((2, 5)\) and \((7, 3)\) using the Pythagorean Theorem, we first determine the horizontal and vertical distances:

1. **Calculate the differences in the coordinates**:
- The horizontal distance (difference in x-coordinates):
\[
x_2 - x_1 = 7 - 2 = 5
\]
- The vertical distance (difference in y-coordinates):
\[
y_2 - y_1 = 3 - 5 = -2 \quad \text{(we will take the absolute value)}
\]
- The absolute value of the vertical distance is:
\[
|-2| = 2
\]

2. **Apply the Pythagorean Theorem**:
The distance \(d\) can be calculated using:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substituting the distances:
\[
d = \sqrt{(5)^2 + (2)^2} = \sqrt{25 + 4} = \sqrt{29}
\]

3. **Calculate \(\sqrt{29}\)**:
\[
\sqrt{29} \approx 5.385
\]

Rounding to the nearest hundredth gives us:
\[
5.39
\]

Thus, the length between the points \((2, 5)\) and \((7, 3)\) is approximately \(5.39\).

The correct response is **5.39**.