To find the distance between the points \((9, 2)\) and \((3, 6)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (9, 2)\) and \((x_2, y_2) = (3, 6)\).
Substituting in the values:
\[ d = \sqrt{(3 - 9)^2 + (6 - 2)^2} \] \[ d = \sqrt{(-6)^2 + (4)^2} \] \[ d = \sqrt{36 + 16} \] \[ d = \sqrt{52} \]
Now, we simplify \(\sqrt{52}\):
\[ \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13} \]
Next, we calculate \(\sqrt{13}\) with a calculator or approximate value, which is approximately \(3.60555\). Therefore,
\[ 2\sqrt{13} \approx 2 \times 3.60555 \approx 7.2111 \]
Rounding this to the nearest tenth gives us:
\[ 7.2 \text{ units} \]
Thus, the distance between the points \((9, 2)\) and \((3, 6)\) is approximately \(7.2\) units.
The answer is:
• 7.2 units