Question

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

Answer 1

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**