Apply the Pythagorean Theorem to find the length between (−1, 6) and (5, −2) . Round your answer to the nearest hundredth, if necessary

Answer 1

We can use the Pythagorean Theorem to find the length between two points in a coordinate plane. The formula is:

c² = a² + b²

where c represents the hypotenuse of a right triangle and a and b represent the lengths of the other two sides.

In this case, the coordinates of the points are (-1, 6) and (5, -2). We can calculate the lengths of the two sides of the right triangle formed:

Side a = 5 - (-1) = 6

Side b = -2 - 6 = -8

Now we can use the Pythagorean Theorem to find the length of the hypotenuse (c):

c² = (6)² + (-8)²
c² = 36 + 64
c² = 100

Taking the square root of both sides, we find:

c ≈ √100
c ≈ 10

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