Question
apply the Pythagorean theorem to find the length between (2, 5) and (7, 3) round the answer to the nearest hundredth
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GPT 3.5
To find the distance between points (2, 5) and (7, 3) using the Pythagorean theorem, we can consider the coordinates as the lengths of the sides of a right triangle.
The horizontal distance (or the base) is the difference between the x-coordinates: 7 - 2 = 5.
The vertical distance (or the height) is the difference between the y-coordinates: 3 - 5 = -2.
Using these distances as the sides of a right triangle, we can find the hypotenuse, which represents the distance between the two points.
Using the Pythagorean theorem, which 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," we can calculate the distance as follows:
Distance^2 = base^2 + height^2
= 5^2 + (-2)^2
= 25 + 4
= 29
Taking the square root of both sides gives:
Distance = √29
Rounding to the nearest hundredth:
Distance ≈ 5.39
The horizontal distance (or the base) is the difference between the x-coordinates: 7 - 2 = 5.
The vertical distance (or the height) is the difference between the y-coordinates: 3 - 5 = -2.
Using these distances as the sides of a right triangle, we can find the hypotenuse, which represents the distance between the two points.
Using the Pythagorean theorem, which 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," we can calculate the distance as follows:
Distance^2 = base^2 + height^2
= 5^2 + (-2)^2
= 25 + 4
= 29
Taking the square root of both sides gives:
Distance = √29
Rounding to the nearest hundredth:
Distance ≈ 5.39
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