Question

Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) . Round your answer to the nearest hundredth, if necessary.

Answer 1

To find the length between two points using the Pythagorean theorem, we need to calculate the difference in the x-coordinates (horizontal distance) and the difference in the y-coordinates (vertical distance).

Let's label the coordinates as follows:
Point 1: (x1, y1) = (2, 5)
Point 2: (x2, y2) = (7, 3)

The horizontal distance (dx) is given by:
dx = x2 - x1 = 7 - 2 = 5

The vertical distance (dy) is given by:
dy = y2 - y1 = 3 - 5 = -2

Now, we can use the Pythagorean theorem to find the length (d) between the two points:
d = √(dx² + dy²)
= √(5² + (-2)²)
= √(25 + 4)
= √29

Rounded to the nearest hundredth, the length between (2, 5) and (7, 3) is approximately 5.39.