Question
Apply the Pythagorean Theorem to find the length between (2,1) and (6,9) Round your answer to the nearest hundredth, if necessary.(1 point)
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GPT 3.5
To find the length between (2,1) and (6,9), we can use the Pythagorean Theorem which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's call the length between (2,1) and (6,9) as d.
The x-coordinate of the first point is 2 and the x-coordinate of the second point is 6. So, the horizontal distance between the two points is 6 - 2 = 4.
The y-coordinate of the first point is 1 and the y-coordinate of the second point is 9. So, the vertical distance between the two points is 9 - 1 = 8.
Using the Pythagorean Theorem, we have:
d^2 = (4)^2 + (8)^2
d^2 = 16 + 64
d^2 = 80
To find the length d, we take the square root of both sides:
d = √80
To round the answer to the nearest hundredth, we evaluate the square root:
d ≈ 8.94
Therefore, the length between (2,1) and (6,9) is approximately 8.94 units.
Let's call the length between (2,1) and (6,9) as d.
The x-coordinate of the first point is 2 and the x-coordinate of the second point is 6. So, the horizontal distance between the two points is 6 - 2 = 4.
The y-coordinate of the first point is 1 and the y-coordinate of the second point is 9. So, the vertical distance between the two points is 9 - 1 = 8.
Using the Pythagorean Theorem, we have:
d^2 = (4)^2 + (8)^2
d^2 = 16 + 64
d^2 = 80
To find the length d, we take the square root of both sides:
d = √80
To round the answer to the nearest hundredth, we evaluate the square root:
d ≈ 8.94
Therefore, the length between (2,1) and (6,9) is approximately 8.94 units.
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