Apply the Pythagorean theorem to find the length of (3, 2) and (7, 8)
To apply the Pythagorean theorem, we need to find the distance between two points on a coordinate plane.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the distance between the points (3, 2) and (7, 8) is the hypotenuse of a right-angled triangle with the other two sides parallel to the x-axis and y-axis.
Using the distance formula, we can calculate the length of the x-side and y-side:
x-side: (7 - 3) = 4
y-side: (8 - 2) = 6
Now we can apply the Pythagorean theorem to find the length of the hypotenuse:
(length of hypotenuse)^2 = (x-side)^2 + (y-side)^2
(length of hypotenuse)^2 = 4^2 + 6^2
(length of hypotenuse)^2 = 16 + 36
(length of hypotenuse)^2 = 52
To find the actual length of the hypotenuse, we take the square root of both sides:
length of hypotenuse = √52
Simplifying, we get:
length of hypotenuse ≈ 7.211
Therefore, the length between the points (3, 2) and (7, 8) is approximately 7.211 units.