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9 of 159 of 15 Items 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) Responses 10.0 units 10.0 units 7.8 units 7.8 units 7.2 units 7.2 units Skip to navigation page 1 of 1

Answer 1

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

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

Where \((x_1, y_1)\) are the coordinates of the first point and \((x_2, y_2)\) are the coordinates of the second point.

For the points (9, 2) and (3, 6):

- \(x_1 = 9\), \(y_1 = 2\)
- \(x_2 = 3\), \(y_2 = 6\)

Now, plug these values into the formula:

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

To simplify \(\sqrt{52}\):

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

Now, calculating the approximate value of \(d\):

\[
\sqrt{13} \approx 3.605551275
\]
\[
d \approx 2 \times 3.605551275 \approx 7.21110255
\]

Rounding to the nearest tenth:

\[
d \approx 7.2 \text{ units}
\]

Thus, the distance between the two points, rounded to the nearest tenth of a unit, is \(7.2\) units.