Lulu marks the points (9, 2) and (3, 6) on the coordinate plane. What is the distance between these two points, rounded to the nearest tenth of a unit?

(1 point)
• 6.0 units
• 7.8 units
• 10.0 units
• 7.2 units

1 answer

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