To find the distance between two points using the Pythagorean theorem, we need to find the lengths of the horizontal and vertical sides of the right triangle formed by the two points.
The horizontal side is the difference between the x-coordinates of the two points: 7 - 3 = 4.
The vertical side is the difference between the y-coordinates of the two points: 8 - 2 = 6.
Now we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse (the longest side).
In this case, the length of the hypotenuse squared is equal to the sum of the squares of the horizontal and vertical sides:
(4^2) + (6^2) = 16 + 36 = 52.
To find the length of the hypotenuse (the distance between the two points), we take the square root of 52:
√52 ≈ 7.21.
Rounded to the nearest hundredth, the length between the two points is approximately 7.21 units.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth. The two points are (3,2) and (7,8)
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