Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.

Question

(1 point)

(6 , 9) ( 2 , 1 )

Answer 1

To find the distance between the two points (6, 9) and (2, 1), we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right 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 lengths of the other two sides.

In this case, we can treat the distance between the points as the hypotenuse of a right triangle, with the horizontal and vertical distances as the other two sides.

The horizontal distance is the difference between the x-coordinates of the two points:
6 - 2 = 4

The vertical distance is the difference between the y-coordinates of the two points:
9 - 1 = 8

Now we can calculate the length between the two points using the Pythagorean theorem:

distance = √(horizontal distance² + vertical distance²)
distance = √(4² + 8²)
distance = √(16 + 64)
distance = √80
distance ≈ 8.94

Rounding to the nearest hundredth, the length between the two points is approximately 8.94 units.

Answer 2

is this correct

Answer 3

Yes, the calculation is correct. The length between the two points is approximately 8.94 units when rounded to the nearest hundredth.