Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth. (3, 2) and (7, 8)

Answer 1

To find the length between the two points (3, 2) and (7, 8), we can use the Pythagorean theorem formula:

c² = a² + b²

First, we need to find the lengths of the horizontal and vertical sides of the right triangle formed by the two points.

Horizontal side (a):
x₂ - x₁ = 7 - 3 = 4

Vertical side (b):
y₂ - y₁ = 8 - 2 = 6

Now, we can substitute these values into the Pythagorean theorem formula:

c² = 4² + 6²
c² = 16 + 36
c² = 52

To find the length (c), we take the square root of both sides:

c = sqrt(52)
c ≈ 7.21

Rounded to the nearest hundredth, the length between the two points (3, 2) and (7, 8) is approximately 7.21.