Apply the Pythagorean Theorem to find the length between (3,2) and (7,8) points. Round your answer to the nearest hundredth.
The distance between two points (x1, y1) and (x2, y2) can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
In this case, the coordinates of the two points are (3, 2) and (7, 8), which can be represented as (x1, y1) = (3, 2) and (x2, y2) = (7, 8).
Using the formula, the length between these two points is given by the equation:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the given values:
d = sqrt((7 - 3)^2 + (8 - 2)^2)
= sqrt(4^2 + 6^2)
= sqrt(16 + 36)
= sqrt(52)
Rounding to the nearest hundredth, the length between these two points is approximately:
d ≈ 7.21