Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3)

Question

. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

29
29
4.58
4.58
5.39
5.39
2.65

Answer 1

To use the Pythagorean Theorem to find the distance between the two points \((2, 5)\) and \((7, 3)\), we can apply the distance formula:

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

Here, \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (7, 3)\).

1. Calculate the differences:

   • \(x_2 - x_1 = 7 - 2 = 5\)
   • \(y_2 - y_1 = 3 - 5 = -2\)

2. Plug these values into the distance formula: \[ d = \sqrt{(5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} \]

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 5.39.