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?

A. 6.0 units
B. 10.0 units
C. 7.8 units
D. 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 the coordinates into the formula:

\[
d = \sqrt{(3 - 9)^2 + (6 - 2)^2}
\]

Calculating the differences:

\[
3 - 9 = -6 \implies (-6)^2 = 36
\]
\[
6 - 2 = 4 \implies 4^2 = 16
\]

Now substituting these values back into the distance formula:

\[
d = \sqrt{36 + 16} = \sqrt{52}
\]

Now, we need to simplify \(\sqrt{52}\). We can factor it:

\[
\sqrt{52} = \sqrt{4 \times 13} = \sqrt{4} \times \sqrt{13} = 2\sqrt{13}
\]

To find the numerical value of \(2\sqrt{13}\), we first approximate \(\sqrt{13}\):

\(\sqrt{13} \approx 3.60555\), so:

\[
2\sqrt{13} \approx 2 \times 3.60555 \approx 7.2111
\]

Rounding to the nearest tenth, we get:

\[
7.2
\]

Thus, the distance between the two points, rounded to the nearest tenth of a unit, is:

\[
\boxed{7.2} \text{ units}
\]