Question

Apply the Pythagorean Theorem to find the length between the two points (7,8) and (3,2). Round your answer to the nearest hundredth.

Answer 1

The coordinates of the two points are (7,8) and (3,2).

The distance between these two points can be found using the Pythagorean theorem, which 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.

We can think of the distance between the two points as the hypotenuse of a right triangle, with the other two sides being the horizontal and vertical distances between the points.

The horizontal distance between the points can be found by subtracting the x-coordinates: 7 - 3 = 4.

The vertical distance between the points can be found by subtracting the y-coordinates: 8 - 2 = 6.

So, we have a right triangle with a horizontal side of length 4 and a vertical side of length 6.

Using the Pythagorean theorem, we can find the length of the hypotenuse (distance between the two points):

c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

c^2 = 4^2 + 6^2
c^2 = 16 + 36
c^2 = 52

Taking the square root of both sides, we find:

c = √52

Rounding to the nearest hundredth, we have:

c ≈ 7.21

Therefore, the distance between the points (7,8) and (3,2) is approximately 7.21.