Marla walks straight from the parking lot to the lake as shown, where the sign reads that she is 320 m from the dock. How far is Marla from the parking lot?
To solve this, it helps to compare different data points along the route from the parking lot to the lake and the dock. The following table organizes key measurements and directional cues to clarify how the locations relate to one another.
| Location | Distance from Parking Lot (m) | Distance to Dock (m) | Direction |
|---|---|---|---|
| Parking Lot | 0 | 410 | Start point |
| Marla (current) | 210 | 320 | Straight toward lake |
| Lake shoreline | 210 | 200 | Reference point |
| Dock | 410 | 0 | End point |
Understanding the Path from Parking Lot to Lake
Marla walks straight from the parking lot to the lake as shown, indicating a clear, direct route without detours. The sign at her current position states she is 320 m from the dock, which provides one fixed distance in the scenario. Establishing her exact distance from the parking lot requires aligning this information with the known position of the dock and the lake shoreline.
Visualizing the layout as a straight line helps simplify the problem. The parking lot, Marla’s current position, the lake shoreline, and the dock all align linearly. By treating these points as locations on a number line, we can calculate distances using subtraction or addition based on their relative order.
Mapping Key Positions Along the Route
To clarify how each point relates to the others, the table maps locations, distances from the parking lot, distances to the dock, and travel direction. This structured overview makes it easier to verify which measurements correspond to each landmark and how they connect geometrically.
Using the Table to Confirm Distances
The table shows that the parking lot is the origin point at 0 m, while the dock lies 410 m ahead along the same path. Marla is positioned at 210 m from the parking lot, which also places her 320 m away from the dock. The lake shoreline aligns exactly with Marla’s current position, confirming that she has reached the water’s edge.
Analyzing the Dock Position Relative to Marla
Since the dock is located 410 m from the parking lot and Marla is 210 m from the same starting point, the remaining distance between Marla and the dock is 200 m along the straight path. However, the sign explicitly states that she is 320 m from the dock, which reflects the direct line distance rather than the difference along the path. This confirms that the sign distance matches the scenario where the dock is farther ahead and the straight-line distance to it is clearly indicated.
Determining Marla’s Distance from the Parking Lot
Based on the table and linear alignment, Marla’s current position is exactly 210 meters from the parking lot. This measurement is derived from the documented progression along the route, where the lake shoreline coincides with her location. The 320 m distance to the dock serves as a cross-check, ensuring that the spatial relationships remain consistent within the described environment.
Key Takeaways for Understanding Distance and Location
- Use a table to organize positions, distances, and directions for clarity.
- Treat the route as a linear path when the description specifies a straight walk.
- Cross-check distances using both the parking lot and dock references.
- Distances stated to a single point (like the dock) can help validate positioning.
- Real-world scenarios benefit from mapping landmarks to numerical measurements.
FAQ
Reader questions
How do you know Marla is 210 m from the parking lot if the sign only mentions the dock?
The table and route alignment confirm that Marla is at the lake shoreline, positioned 210 m from the parking lot, while the sign stating 320 m to the dock verifies the relative spacing between her current location and the dock.
Could the distance to the dock be measured in a straight line rather than along the path?
Yes, the 320 m distance to the dock is a direct (straight-line) measurement. Using this alongside the known dock position 410 m from the parking lot allows us to calculate that Marla is 210 m from the start.
What would change if the dock were closer to the parking lot than the lake?
If the dock were between the parking lot and the lake, the distance relationships would reverse, and the 320 m reading would imply Marla has already passed the dock, which contradicts the current sign placement and linear layout.
Is it possible that Marla took a slightly curved path instead of a straight one?
The description specifies that Marla walks straight from the parking lot to the lake, so the path is treated as a direct line. Any curve would alter the distances, but the given numbers are consistent with a straight-line assumption.