Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth. (-2,-1) (2,4)
To find the distance between the two points (-2,-1) and (2,4), we can use the Pythagorean Theorem which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
First, we need to find the lengths of the two sides of the right triangle formed by the two points:
Length of horizontal side = 2 - (-2) = 4
Length of vertical side = 4 - (-1) = 5
Now, we can use the Pythagorean Theorem to find the length of the hypotenuse:
a^2 + b^2 = c^2
4^2 + 5^2 = c^2
16 + 25 = c^2
41 = c^2
c = √41 ≈ 6.40
Therefore, the distance between the two points (-2,-1) and (2,4) is approximately 6.40 units.