To solve this problem, let's break it down into the two parts: distance covered and displacement.
1. Distance Covered:
- Alexis walks 10 km west to get to the grocery store.
- After shopping, she walks 10 km back east to return to her house.
- To find the total distance covered, we add the distances for each leg of the journey:
[tex]\[
\text{Total Distance} = 10 \, \text{km (to the store)} + 10 \, \text{km (back home)} = 20 \, \text{km}
\][/tex]
2. Displacement:
- Displacement is the net change in position, which is a vector quantity that gives the shortest distance between the starting and ending points, along with the direction.
- Alexis starts at her house and ends up back at her house.
- Since she starts and ends at the same point, the net change in position is zero.
[tex]\[
\text{Displacement} = 0 \, \text{km}
\][/tex]
So, the total distance covered is 20 km, and the displacement is 0 km.
Therefore, the correct answer is:
```
distance = 20 km, displacement = 0 km
```
