Question

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary. (2, -3), (5,5)

(1 point)
Responses

11
11

8.54
8.54

73
73

7.62

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the distance between the two points (2, -3) and (5, 5), 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 distance between the two points will be the length of the hypotenuse of a right triangle formed by these two points.

The length of the horizontal side of the triangle can be found by subtracting the x-coordinates of the two points: 5 - 2 = 3.
The length of the vertical side of the triangle can be found by subtracting the y-coordinates of the two points: 5 - (-3) = 8.

Using the Pythagorean Theorem, we have:

hypotenuse^2 = horizontal side^2 + vertical side^2
hypotenuse^2 = 3^2 + 8^2
hypotenuse^2 = 9 + 64
hypotenuse^2 = 73

Taking the square root of both sides, we have:

hypotenuse ≈ √73 ≈ 8.54

So, the length between the two points is approximately 8.54.

Therefore, the correct answer is 8.54.