To find the distance between the points \((9, 2)\) and \((3, 6)\) on the coordinate plane, we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, we can assign the coordinates as follows:
- \((x_1, y_1) = (9, 2)\)
- \((x_2, y_2) = (3, 6)\)
Now, we plug in the values into the distance formula:
\[ d = \sqrt{(3 - 9)^2 + (6 - 2)^2} \]
Calculating the differences:
\[ 3 - 9 = -6 \quad \text{and} \quad 6 - 2 = 4 \]
Now substitute these values back into the formula:
\[ d = \sqrt{(-6)^2 + (4)^2} \]
Calculating the squares gives:
\[ d = \sqrt{36 + 16} \]
Now, add the two values:
\[ d = \sqrt{52} \]
Next, we can simplify \(\sqrt{52}\):
\[ \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13} \]
Now, we will calculate the approximate value of \(\sqrt{13}\). We know that:
\[ \sqrt{13} \approx 3.605 \]
Thus, we have:
\[ d \approx 2 \times 3.605 \approx 7.21 \]
Finally, rounding 7.21 to the nearest tenth gives us:
\[ \boxed{7.2} \]
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