Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth. (5, 5) and (2, -3)
To find the length between the two points (5, 5) and (2, -3), we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
The length between the two points can be found as follows:
1. Find the horizontal distance between the two points:
distance_x = 5 - 2 = 3
2. Find the vertical distance between the two points:
distance_y = 5 - (-3) = 8
3. Calculate the length by applying the Pythagorean Theorem:
length = √(distance_x^2 + distance_y^2)
= √(3^2 + 8^2)
= √(9 + 64)
= √73
To the nearest hundredth, the length between the two points is approximately 8.54.