Apply the Pythagorean Theorem to find the length between the two points 7,8 and 3,2. Round your answer to the nearest hundredth.
To find the length between two points using the Pythagorean theorem, we need to find the length of the legs of a right triangle with those points as its vertices.
The coordinates of the two points are (7,8) and (3,2). Using the distance formula, we can find the length of the legs:
Leg 1: (x1, y1) = (7, 8)
Leg 2: (x2, y2) = (3, 2)
Using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's plug in the values:
d = sqrt((3 - 7)^2 + (2 - 8)^2)
d = sqrt((-4)^2 + (-6)^2)
d = sqrt(16 + 36)
d = sqrt(52)
Now, we need to round our answer to the nearest hundredth:
d ≈ 7.21
Therefore, the length between the two points (7,8) and (3,2) is approximately 7.21 units.