Question
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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GPT 3.5
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.
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.
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