Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) . Round your answer to the nearest hundredth, if necessary.(1 point) Responses 2.65 2.65 29 29 4.58 4.58 5.39
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GPT-4o mini
To find the distance between the points \((2, 5)\) and \((7, 3)\) using the distance formula, which is derived from the Pythagorean Theorem, we can use the formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Where \((x_1, y_1)\) is \((2, 5)\) and \((x_2, y_2)\) is \((7, 3)\).
Now substitute the values into the formula:
\[
d = \sqrt{(7 - 2)^2 + (3 - 5)^2}
\]
\[
= \sqrt{(5)^2 + (-2)^2}
\]
\[
= \sqrt{25 + 4}
\]
\[
= \sqrt{29}
\]
Calculating the square root of 29 gives us:
\[
d \approx 5.385
\]
Rounding to the nearest hundredth, the distance is approximately:
\[
d \approx 5.39
\]
Thus, the length between the points \((2, 5)\) and \((7, 3)\) is **5.39**.
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Where \((x_1, y_1)\) is \((2, 5)\) and \((x_2, y_2)\) is \((7, 3)\).
Now substitute the values into the formula:
\[
d = \sqrt{(7 - 2)^2 + (3 - 5)^2}
\]
\[
= \sqrt{(5)^2 + (-2)^2}
\]
\[
= \sqrt{25 + 4}
\]
\[
= \sqrt{29}
\]
Calculating the square root of 29 gives us:
\[
d \approx 5.385
\]
Rounding to the nearest hundredth, the distance is approximately:
\[
d \approx 5.39
\]
Thus, the length between the points \((2, 5)\) and \((7, 3)\) is **5.39**.
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