Apply the Pythagorean Theorem to find the length between (3,2) and (7,8) points. Round your answer to the nearest hundredth
To find the length between two points using the Pythagorean Theorem, we need to calculate the square root of the sum of the squares of the differences in their coordinates.
The coordinates of the first point are (3,2), and the coordinates of the second point are (7,8).
Let's calculate the differences in their x-coordinates and y-coordinates:
Δx = 7 - 3 = 4
Δy = 8 - 2 = 6
Now, square these differences:
(Δx)² = 4² = 16
(Δy)² = 6² = 36
Next, sum the squares:
(Δx)² + (Δy)² = 16 + 36 = 52
Finally, calculate the square root to find the length:
√(Δx)² + (Δy)² = √52 ≈ 7.21
Rounded to the nearest hundredth, the length between the points (3,2) and (7,8) is approximately 7.21.