Question

Apply the Pythagorean Theorem to find the length Between the two points (2,-3) and (5,5). Round your answer to the nearest hundredth if necessary. The points are (-2, -1) and (2, 4)

Answer 1

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

For the first set of points, we have:
Horizontal leg = 5 - 2 = 3
Vertical leg = 5 - (-3) = 8

Using the Pythagorean Theorem, we can calculate the length of the hypotenuse:
Hypotenuse = √(3^2 + 8^2) = √(9 + 64) = √73

Rounded to the nearest hundredth, the length between the points (2,-3) and (5,5) is approximately 8.54.

For the second set of points, we have:
Horizontal leg = 2 - (-2) = 4
Vertical leg = 4 - (-1) = 5

Using the Pythagorean Theorem, we can calculate the length of the hypotenuse:
Hypotenuse = √(4^2 + 5^2) = √(16 + 25) = √41

Rounded to the nearest hundredth, the length between the points (-2,-1) and (2,4) is approximately 6.40.