Question

Carla is playing hide-and-seek with Marvin and Liz. Marvin is hiding 24 meters south of Carla, and Liz is hiding 10 meters east of Marvin. How far apart are Carla and Liz?

meters

Answer 1

To find the distance between Carla and Liz, we can use the coordinates based on their given positions. Let's set Carla's position as the origin point (0, 0).

- Since Marvin is hiding 24 meters south of Carla, his position will be (0, -24) (where south is negative on the y-axis).
- Liz is hiding 10 meters east of Marvin. Marvin's east-west position is 0, and since Liz is to the east (positive on the x-axis), her position will be (10, -24).

Now we have:
- Carla's position: (0, 0)
- Liz's position: (10, -24)

Next, we can use the distance formula to calculate the distance between Carla and Liz:

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

Substituting in the coordinates of Carla (0, 0) and Liz (10, -24):

\[
d = \sqrt{(10 - 0)^2 + (-24 - 0)^2}
\]
\[
d = \sqrt{(10)^2 + (-24)^2}
\]
\[
d = \sqrt{100 + 576}
\]
\[
d = \sqrt{676}
\]
\[
d = 26
\]

Thus, Carla and Liz are **26 meters apart**.