Question

Apply the Pythagorean Theorem to find the length between(1,5)and(4,8) . Round your answer to the nearest hundredth, if necessary.

Answer 1

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

Let's consider the points (1,5) and (4,8).

The horizontal side length can be found by subtracting the x-coordinates: 4 - 1 = 3.

The vertical side length can be found by subtracting the y-coordinates: 8 - 5 = 3.

Now, we can use the Pythagorean Theorem to calculate the length of the hypotenuse (the distance between the two points):

hypotenuse^2 = (horizontal side length)^2 + (vertical side length)^2

hypotenuse^2 = 3^2 + 3^2
hypotenuse^2 = 9 + 9
hypotenuse^2 = 18

Taking the square root of both sides, we find:

hypotenuse = √18 ≈ 4.24

Therefore, the length between the points (1,5) and (4,8) is approximately 4.24.