Apply the Pythagorean theorem to find the length between (-1,6) an (5,-2) round to the nearest hundredth if necessary

Answer 1

To apply the Pythagorean theorem, we need to find the length of the diagonal line connecting the two given points. The Pythagorean theorem states that the square of the length of the hypotenuse (c) of a right triangle is equal to the sum of the squares of the other two sides (a and b).

First, let's find the length of the horizontal side (a):
a = (5 - (-1)) = 5 + 1 = 6

Next, let's find the length of the vertical side (b):
b = (-2 - 6) = -8

Now, we can apply the Pythagorean theorem to find the length of the diagonal line (c):
c^2 = a^2 + b^2
c^2 = 6^2 + (-8)^2
c^2 = 36 + 64
c^2 = 100
c = √100
c = 10

Therefore, the length between (-1,6) and (5,-2) is 10 units.