Question

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.
responses
9

5.57

41

6.40

(2,4) (-2,-1)

Answer 1

The Pythagorean Theorem is used to find the length of the hypotenuse of a right triangle when the lengths of the other two sides are known. In the context of finding the distance between two points in a plane, the two sides are the differences in the x-coordinates and y-coordinates of the points, while the hypotenuse is the distance between the points.

Given points (2,4) and (-2,-1), let's calculate the differences in the x-coordinates and y-coordinates:

The change in the x-coordinate (Δx) is:
2 - (-2) = 2 + 2 = 4

The change in the y-coordinate (Δy) is:
4 - (-1) = 4 + 1 = 5

Now, we use the Pythagorean Theorem to find the distance d between the points:

d² = Δx² + Δy²
d² = 4² + 5²
d² = 16 + 25
d² = 41

Now we take the square root of 41 to find d:

d = √41
d ≈ 6.40 (rounded to the nearest hundredth)

Therefore, the distance between the points (2,4) and (-2,-1) is approximately 6.40 units.