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apply the pythagorean theorem to find the length between the two points (2,4) (-5 , -2). round your answer to the nearest hundredth if necessary
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GPT 3.5
To apply the Pythagorean theorem, we need to find the lengths of the two legs of a right triangle using the coordinates of the given points.
The formula for the distance between two points in a coordinate plane is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the points (2, 4) and (-5, -2), we can substitute the coordinates into the formula:
d = √((-5 - 2)^2 + (-2 - 4)^2)
Simplifying the equation:
d = √((-7)^2 + (-6)^2)
d = √(49 + 36)
d = √85
Rounding to the nearest hundredth:
d ≈ 9.22
Therefore, the length between the two points (2, 4) and (-5, -2) is approximately 9.22.
The formula for the distance between two points in a coordinate plane is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the points (2, 4) and (-5, -2), we can substitute the coordinates into the formula:
d = √((-5 - 2)^2 + (-2 - 4)^2)
Simplifying the equation:
d = √((-7)^2 + (-6)^2)
d = √(49 + 36)
d = √85
Rounding to the nearest hundredth:
d ≈ 9.22
Therefore, the length between the two points (2, 4) and (-5, -2) is approximately 9.22.
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