Question

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses

9
9

6:40
6:40

41
41

5.57


The coordinates are; (-2,4)

Answer 1

and (3,-2).

To apply the Pythagorean Theorem, we need to find the length of the horizontal and vertical legs of the right triangle formed by the two points.

The horizontal leg is the difference between the x-coordinates of the two points:
horizontal leg = 3 - (-2) = 5

The vertical leg is the difference between the y-coordinates of the two points:
vertical leg = -2 - 4 = -6

To find the length between the two points, we can use the formula:
length = √(horizontal leg^2 + vertical leg^2)

Substituting the values:
length = √(5^2 + (-6)^2)

Calculating:
length = √(25 + 36) = √61

Rounding to the nearest hundredth:
length ≈ 7.81

Therefore, the length between the two points (-2,4) and (3,-2) is approximately 7.81.