The Pythagorean Theorem 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.
To find the distance between points (-1,6) and (5,-2), we need to treat these points as the coordinates of the endpoints of a right triangle in a coordinate plane.
Let's label the points: (-1,6) as point A and (5,-2) as point B.
The length of the horizontal side of the triangle (also known as the base or the difference in x-coordinates) is given by the absolute difference of the x-coordinates of the two points:
Δx = |5 - (-1)| = 6
The length of the vertical side of the triangle (also known as the height or the difference in y-coordinates) is given by the absolute difference of the y-coordinates of the two points:
Δy = |-2 - 6| = 8
Now, using the Pythagorean Theorem, we can find the length of the hypotenuse (the distance between points A and B):
c² = a² + b²
Plug in the values:
c² = 6² + 8²
c² = 36 + 64
c² = 100
Taking the square root of both sides:
c = √100
c = 10
Therefore, the length between points (-1,6) and (5,-2) is 10 units.
Apply the Pythagorean Theorem to find the length Between (-1,6) and (5,-2). Round your answer to the nearest hundredth if necessary.
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