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?

Answer 1

To find the distance between the points \((9, 2)\) and \((3, 6)\) in the coordinate plane, we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

In this case, we can assign:
- \((x_1, y_1) = (9, 2)\)
- \((x_2, y_2) = (3, 6)\)

Now, we substitute these coordinates into the formula:

\[
d = \sqrt{(3 - 9)^2 + (6 - 2)^2}
\]
\[
= \sqrt{(-6)^2 + (4)^2}
\]
\[
= \sqrt{36 + 16}
\]
\[
= \sqrt{52}
\]

Next, we simplify \(\sqrt{52}\):

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

Now we need to find the approximate value of \(\sqrt{13}\). Using a calculator, we find that:

\[
\sqrt{13} \approx 3.60555
\]

So,

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

Finally, rounding to the nearest tenth:

\[
7.2111 \approx 7.2
\]

Thus, the distance between the points \((9, 2)\) and \((3, 6)\) is approximately \(\boxed{7.2}\) units.