Question

apply the pythagorean theorem to find the length between the two points (5,5) (2, -3). 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 find the lengths of the horizontal and vertical sides of the right triangle formed by the two points.

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

Now, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the distance between the two points.

Applying the Pythagorean theorem:
distance^2 = horizontal side^2 + vertical side^2
distance^2 = 3^2 + 8^2
distance^2 = 9 + 64
distance^2 = 73

To find the distance, we need to take the square root of both sides of the equation:
distance = sqrt(73)

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