To find the distance between the points \((2, 5)\) and \((7, 3)\), we can use the distance formula, which is based on 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 \((x_2, y_2) = (7, 3)\).
First, calculate the differences:
\[ x_2 - x_1 = 7 - 2 = 5 \] \[ y_2 - y_1 = 3 - 5 = -2 \]
Now substitute these values into the distance formula:
\[ d = \sqrt{(5)^2 + (-2)^2} \] \[ d = \sqrt{25 + 4} \] \[ d = \sqrt{29} \]
Now, calculate \(\sqrt{29}\):
\(\sqrt{29} \approx 5.385\)
Rounding to the nearest hundredth gives:
\[ d \approx 5.39 \]
So, the distance between the points \((2, 5)\) and \((7, 3)\) is approximately 5.39.
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