Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.
Given distances on graph (7, 8) and (3, 2).
To find the length between the two points (7, 8) and (3, 2), we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Using the given points, we can calculate the length between them by finding the difference in their x-coordinates and the difference in their y-coordinates.
Let's call the first point (x1, y1) = (7, 8) and the second point (x2, y2) = (3, 2).
The difference in x-coordinates (Δx) is x2 - x1 = 3 - 7 = -4.
The difference in y-coordinates (Δy) is y2 - y1 = 2 - 8 = -6.
We can use Δx and Δy to find the length between the two points, which is the hypotenuse of a right triangle.
Using the Pythagorean Theorem, the length (L) is given by:
L = √(Δx^2 + Δy^2)
Plugging in the values, we get:
L = √((-4)^2 + (-6)^2)
= √(16 + 36)
= √52
Rounding to the nearest hundredth, the length between the two points is approximately 7.21.