https://file.aiquickdraw.com/mathbot/file/1727210989145api7b7qn.jpg

Let's break down the problem step by step from your image:

### a. Forward 5 steps:
The distance walked is **2.90 meters**.

### b. Turn 90° left and walk 2 steps:
The distance walked here is **1.50 meters**.

### c. Turn 90° left and walk 3 steps:
The distance walked here is **1.75 meters**.

### d. Turn 90° left and walk 4 steps:
The distance walked here is **2.10 meters**.

### e. Draw vector arrows:
The image shows a closed path in the shape of a rectangle, with arrows representing each part of the walk.

---

### f. Measured Displacement:
Displacement is the straight-line distance from the origin to the final position. Since the shape in the diagram is a closed rectangle, and you end where you started, the **measured displacement** is **0 meters**.

### g. Total Distance:
The total distance is the sum of all the individual distances:
\[
\text{Distance} = 2.90 \, m + 1.50 \, m + 1.75 \, m + 2.10 \, m = 8.25 \, \text{meters}
\]

### h. Calculated Displacement:
Since the path forms a complete rectangle and ends back at the origin, the calculated displacement (straight-line distance from start to end) is also **0 meters**. Displacement considers only the initial and final position, and in this case, they are the same.

### i. Comparison:
Yes, the calculated displacement matches the measured displacement of **0 meters**. This happens because displacement is a vector quantity that depends only on the initial and final positions, not the actual path taken. Since you returned to the origin, your displacement is zero, even though you walked a total distance of 8.25 meters.

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### Review: Difference Between Distance and Displacement
- **Distance** is a scalar quantity and measures the total length of the path traveled.
- **Displacement** is a vector quantity and measures the straight-line distance between the starting and ending points, along with the direction.

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Let me know if you need further clarification on any part! Here are some follow-up questions to expand your understanding:

1. What would happen to the displacement if you hadn't returned to the origin?
2. How would you calculate displacement if the path wasn't rectangular?
3. What real-life situations could have large distances but zero displacements?
4. Can displacement be greater than the distance traveled?
5. Why is displacement considered a vector while distance is not?

### Tip:
In problems involving vectors, always remember that direction matters for displacement but not for distance.

You are asked to calculate the total distance and displacement after walking a series of steps in different directions (forward, left, etc.). Measurements are provided for each segment, and you need to calculate the total distance and displacement using a vector approach.

Learn how to calculate total distance and displacement from a set of directional steps using vector addition. This exercise involves understanding the difference between distance and displacement, applying the Pythagorean theorem, and analyzing vector components. Suitable for middle school students (Grades 6-9).

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