pply the Pythagorean Theorem to find the length between (−1, -2) and (4,2) . Round y

Answer 1

To find the length between the points (−1, -2) and (4, 2), we can apply the Pythagorean Theorem.

The Pythagorean Theorem 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.

In this problem, we have a right triangle, with the horizontal distance between the points serving as one side (a), the vertical distance between the points serving as the other side (b), and the length between the points serving as the hypotenuse (c).

a = 4 - (-1) = 5
b = 2 - (-2) = 4

Using the Pythagorean Theorem, we can find the length between the points:

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

To find the length (c), we take the square root:

c = √41

Rounding this value to two decimal places, the length between the points is approximately 6.40.