apply the pythagorean theorem to find the length between the two points (2,4) (-5 , -2). round your answer to the nearest hundredth if necessary

Answer 1

To apply the Pythagorean theorem, we need to find the lengths of the two legs of a right triangle using the coordinates of the given points.

The formula for the distance between two points in a coordinate plane is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the points (2, 4) and (-5, -2), we can substitute the coordinates into the formula:

d = √((-5 - 2)^2 + (-2 - 4)^2)

Simplifying the equation:

d = √((-7)^2 + (-6)^2)

d = √(49 + 36)

d = √85

Rounding to the nearest hundredth:

d ≈ 9.22

Therefore, the length between the two points (2, 4) and (-5, -2) is approximately 9.22.