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

Question

2,4 and -2,-1

Answer 1

To apply the Pythagorean Theorem, we need to find the distances between the x-coordinates and the y-coordinates of the two points.

The x-coordinates are 2 and -2, so the difference is 2 - (-2) = 4.
The y-coordinates are 4 and -1, so the difference is 4 - (-1) = 5.

Using the Pythagorean Theorem, the length between the two points (2,4) and (-2,-1) can be found as follows:

c^2 = a^2 + b^2

where c is the length between the two points, and a and b are the differences between the corresponding coordinates.

c^2 = 4^2 + 5^2
c^2 = 16 + 25
c^2 = 41

To find c, we take the square root of both sides of the equation:

c = √(41)

Rounding to the nearest hundredth, the length between the two points is approximately 6.40.

Answer 2

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
A (2,-3) B(5,5)

Answer 3

To apply the Pythagorean Theorem, we need to find the distances between the x-coordinates and the y-coordinates of the two points.

The x-coordinate difference is 5 - 2 = 3.
The y-coordinate difference is 5 - (-3) = 8.

Using the Pythagorean Theorem, the length between the two points A(2, -3) and B(5, 5) is found as follows:

c^2 = a^2 + b^2

where c is the length between the two points, and a and b are the differences between the corresponding coordinates.

c^2 = 3^2 + 8^2
c^2 = 9 + 64
c^2 = 73

To find c, we take the square root of both sides of the equation:

c = √73

Rounding to the nearest hundredth, the length between the two points is approximately 8.54 units.