Question

Apply the Pythagorean Theorem to
find the length between (2, 5) and (7, 3)
. Round your answer to the
nearest hundredth, if necessary.

Answer 1

To find the distance between the points \((2, 5)\) and \((7, 3)\) using the Pythagorean theorem, we can follow these steps:

1. **Identify the coordinates**:
- Point A: \((x_1, y_1) = (2, 5)\)
- Point B: \((x_2, y_2) = (7, 3)\)

2. **Calculate the differences in the coordinates**:
- Difference in x-coordinates:
\[
x_2 - x_1 = 7 - 2 = 5
\]
- Difference in y-coordinates:
\[
y_2 - y_1 = 3 - 5 = -2
\]

3. **Use the Pythagorean theorem to find the distance**:
The distance \(d\) between two points is given by the formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Plugging in the differences:
\[
d = \sqrt{(5)^2 + (-2)^2}
\]
\[
d = \sqrt{25 + 4}
\]
\[
d = \sqrt{29}
\]

4. **Calculate \(\sqrt{29}\)**:
Using a calculator, we get:
\[
d \approx 5.385164807134504
\]

5. **Round to the nearest hundredth**:
The nearest hundredth is:
\[
d \approx 5.39
\]

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