Question

Apply the Pythagorean theorem to find the length of (3, 2) and (7, 8) round your answer to the nearest hundredth

Answer 1

To find the length of the line segment between points (3, 2) and (7, 8), we can apply the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square 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 two points form a right triangle with the line segment between them as the hypotenuse. We can consider the horizontal and vertical distances between the points as the other two sides.

The horizontal distance (Δx) between the points is given by subtracting the x-coordinates:

Δx = 7 - 3 = 4

The vertical distance (Δy) between the points is given by subtracting the y-coordinates:

Δy = 8 - 2 = 6

We can use these side lengths in the Pythagorean theorem equation:

(hypotenuse)^2 = (Δx)^2 + (Δy)^2

(hypotenuse)^2 = 4^2 + 6^2

(hypotenuse)^2 = 16 + 36

(hypotenuse)^2 = 52

To find the length of the line segment (hypotenuse), we take the square root of both sides:

hypotenuse = √52

Using a calculator, we find:

hypotenuse ≈ 7.21

Rounding the answer to the nearest hundredth, the length of the line segment between points (3, 2) and (7, 8) is approximately 7.21.