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)Responses10.0 units10.0 units7.8 units7.8 units7.2 units7.2 units6.0 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, we set:
- \( (x_1, y_1) = (9, 2) \)
- \( (x_2, y_2) = (3, 6) \)

Now, substituting in the values:

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

Now calculate \( \sqrt{52} \):

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

Next, we can approximate \( \sqrt{13} \). The approximate value of \( \sqrt{13} \) is about \( 3.605551275 \), so:

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

Rounding to the nearest tenth, we find:

\[
d \approx 7.2
\]

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