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.
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