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 answer

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:

\[ \boxed{7.2} \]