Question

Kimberly is deep-sea diving with two friends. Jenna is floating on the surface 7 meters above Kimberly, and Clarence is exploring a coral reef 7 meters in front of Kimberly. How far apart are Jenna and Clarence? If necessary, round to the nearest tenth.

meters

Answer 1

To find the distance between Jenna and Clarence, we can visualize the situation in a two-dimensional coordinate system.

1. **Position of Kimberly**: Let’s assume Kimberly is at the origin (0, 0).
2. **Position of Jenna**: Since Jenna is 7 meters above Kimberly, her coordinates would be (0, 7).
3. **Position of Clarence**: Since Clarence is 7 meters in front of Kimberly, his coordinates would be (7, 0).

Now, we can use the distance formula to find the distance \(d\) between Jenna and Clarence, where their coordinates are \( (x_1, y_1) \) and \( (x_2, y_2) \):

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

Substituting in the coordinates of Jenna and Clarence:

- \( (x_1, y_1) = (0, 7) \) for Jenna
- \( (x_2, y_2) = (7, 0) \) for Clarence

So we have:

\[
d = \sqrt{(7 - 0)^2 + (0 - 7)^2}
\]
\[
d = \sqrt{(7)^2 + (-7)^2}
\]
\[
d = \sqrt{49 + 49}
\]
\[
d = \sqrt{98}
\]
\[
d \approx 9.899
\]

Rounding to the nearest tenth, the distance between Jenna and Clarence is approximately:

\[
\boxed{9.9} \text{ meters}
\]