Bot GPT 4-o mini To find the length between the points \((2, 5)\) and \((7, 3)\), we can use the distance formula, which is derived from the Pythagorean Theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (7, 3)\).
Now, we will substitute the values:
\[ d = \sqrt{(7 - 2)^2 + (3 - 5)^2} \]
Calculating the differences:
\[ d = \sqrt{(5)^2 + (-2)^2} \]
Next, we square the differences:
\[ d = \sqrt{25 + 4} \]
Now, add these values:
\[ d = \sqrt{29} \]
Finally, we can calculate the square root:
\[ d \approx 5.385 \]
Rounding to the nearest hundredth, we have:
\[ d \approx 5.39 \]
Thus, the length between the points \((2, 5)\) and \((7, 3)\) is approximately 5.39.
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