Question

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.

Point 1 = (7, 8)
Point 2 = (3, 2)

Answer 1

To find the distance between the two points using the Pythagorean theorem, we need to find the lengths of the adjacent and opposite sides of the right triangle formed by the two points.

The length of the adjacent side (base) can be found by subtracting the x-coordinate of Point 2 from the x-coordinate of Point 1:
Adjacent side = 7 - 3 = 4

The length of the opposite side (height) can be found by subtracting the y-coordinate of Point 2 from the y-coordinate of Point 1:
Opposite side = 8 - 2 = 6

Now that we have the lengths of the two sides, we can use the Pythagorean theorem to find the length of the hypotenuse (distance between the two points):
Hypotenuse^2 = Adjacent side^2 + Opposite side^2

Hypotenuse^2 = 4^2 + 6^2
Hypotenuse^2 = 16 + 36
Hypotenuse^2 = 52

To find the length of the hypotenuse, we take the square root of both sides of the equation:
Hypotenuse = √52 ≈ 7.21

Therefore, the distance between the two points, rounded to the nearest hundredth, is approximately 7.21.