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

4.58
4.58

29
29

5.39
5.39

2.65

Answer 1

To apply the Pythagorean theorem, we need to find the lengths of the two sides of the right triangle formed by the two given points.

The length of the horizontal side is the difference between the x-coordinates: 7 - 2 = 5.

The length of the vertical side is the difference between the y-coordinates: 3 - 5 = -2. Since we only want the length, we take the absolute value: |-2| = 2.

We can now apply the Pythagorean theorem:

c^2 = a^2 + b^2

c^2 = 5^2 + 2^2

c^2 = 25 + 4

c^2 = 29

Taking the square root of both sides gives us:

c ≈ √29

Rounding to the nearest hundredth, c ≈ 5.39.

Therefore, the correct answer is 5.39.