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)

2.65

5.39

29

4.58

Answer 1

To find the length between the points (2, 5) and (7, 3) using the Pythagorean Theorem, we first determine the differences in the x-coordinates and the y-coordinates.

1. Calculate the difference in x-coordinates:
\[
\Delta x = 7 - 2 = 5
\]

2. Calculate the difference in y-coordinates:
\[
\Delta y = 3 - 5 = -2
\]

3. Use the Pythagorean Theorem, which states that the distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
d = \sqrt{(\Delta x)^2 + (\Delta y)^2}
\]

Substituting the values we computed:
\[
d = \sqrt{(5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29}
\]

4. Calculate \(\sqrt{29}\):
\[
d \approx 5.385
\]

Rounding to the nearest hundredth gives:
\[
d \approx 5.39
\]

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