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 \((3, 6)\) on the coordinate plane, we can use the distance formula, which is given by:

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

Here, we can assign the coordinates as follows:
- \((x_1, y_1) = (9, 2)\)
- \((x_2, y_2) = (3, 6)\)

Now, we plug in the values into the distance formula:

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

Calculating the differences:

\[
3 - 9 = -6 \quad \text{and} \quad 6 - 2 = 4
\]

Now substitute these values back into the formula:

\[
d = \sqrt{(-6)^2 + (4)^2}
\]

Calculating the squares gives:

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

Now, add the two values:

\[
d = \sqrt{52}
\]

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

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

Now, we will calculate the approximate value of \(\sqrt{13}\). We know that:

\[
\sqrt{13} \approx 3.605
\]

Thus, we have:

\[
d \approx 2 \times 3.605 \approx 7.21
\]

Finally, rounding 7.21 to the nearest tenth gives us:

\[
\boxed{7.2}
\]