To find the distance between the points \((3, 2)\) and \((7, 8)\) on an xy-graph, 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:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates of the points \((3, 2)\) and \((7, 8)\):
- \(x_1 = 3\)
- \(y_1 = 2\)
- \(x_2 = 7\)
- \(y_2 = 8\)
Now plug in these values into the formula:
\[ d = \sqrt{(7 - 3)^2 + (8 - 2)^2} \] \[ d = \sqrt{(4)^2 + (6)^2} \] \[ d = \sqrt{16 + 36} \] \[ d = \sqrt{52} \]
Now we can calculate \(\sqrt{52}\):
\[ d \approx 7.2111 \]
Rounding this to the nearest hundredth, we get:
\[ d \approx 7.21 \]
So, the distance between the points (3, 2) and (7, 8) is 7.21.
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