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

2.65
2.65

5.39
5.39

29
29

4.58

Answer 1

To find the length between two points using the Pythagorean Theorem, we need to find the horizontal distance (x-distance) and the vertical distance (y-distance) between the points.

The x-distance is calculated by subtracting the x-coordinate of one point from the x-coordinate of the other point:
x-distance = 7 - 2 = 5

The y-distance is calculated by subtracting the y-coordinate of one point from the y-coordinate of the other point:
y-distance = 3 - 5 = -2

Since the Pythagorean Theorem only works with positive distances, we need to take the absolute value of the y-distance:
y-distance = |-2| = 2

Now we can use the Pythagorean Theorem:

length = √((x-distance)^2 + (y-distance)^2)
length = √((5)^2 + (2)^2)
length = √(25 + 4)
length = √29

Rounding to the nearest hundredth, the length between (2, 5) and (7, 3) is approximately 5.39.

Therefore, the correct answer is:
5.39