To find the distance between the points (9, 2) and (3, 6) on the coordinate plane, you can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where \((x_1, y_1)\) are the coordinates of the first point and \((x_2, y_2)\) are the coordinates of the second point.
For the points (9, 2) and (3, 6):
- \(x_1 = 9\), \(y_1 = 2\)
- \(x_2 = 3\), \(y_2 = 6\)
Now, plug these values into the formula:
\[ d = \sqrt{(3 - 9)^2 + (6 - 2)^2} \] \[ d = \sqrt{(-6)^2 + (4)^2} \] \[ d = \sqrt{36 + 16} \] \[ d = \sqrt{52} \]
To simplify \(\sqrt{52}\):
\[ \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13} \]
Now, calculating the approximate value of \(d\):
\[ \sqrt{13} \approx 3.605551275 \] \[ d \approx 2 \times 3.605551275 \approx 7.21110255 \]
Rounding to the nearest tenth:
\[ d \approx 7.2 \text{ units} \]
Thus, the distance between the two points, rounded to the nearest tenth of a unit, is \(7.2\) units.