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, we set:
- \( (x_1, y_1) = (9, 2) \)
- \( (x_2, y_2) = (3, 6) \)
Now, 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 calculate \( \sqrt{52} \):
\[ \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13} \]
Next, we can approximate \( \sqrt{13} \). The approximate value of \( \sqrt{13} \) is about \( 3.605551275 \), so:
\[ 2\sqrt{13} \approx 2 \times 3.605551275 \approx 7.21110255 \]
Rounding to the nearest tenth, we find:
\[ d \approx 7.2 \]
Thus, the distance between the points \( (9, 2) \) and \( (3, 6) \) is approximately 7.2 units.