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
5.39
5.39
2.65
2.65
29
29
4.58
To find the distance between the points (2, 5) and (7, 3), we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides are the horizontal distance and the vertical distance between the points. The horizontal distance can be found by subtracting the x-coordinates of the two points, and the vertical distance can be found by subtracting the y-coordinates.
Horizontal distance = 7 - 2 = 5
Vertical distance = 3 - 5 = -2
Since the horizontal and vertical distances are the two legs of a right triangle, we can use the Pythagorean Theorem to find the length of the hypotenuse (the distance between the points).
Hypotenuse = sqrt((5^2) + (-2^2))
= sqrt(25 + 4)
= sqrt(29)
≈ 5.39
Therefore, the length between (2, 5) and (7, 3) is approximately 5.39. So the correct response is:
5.39