Educational worksheet on distance and displacement, illustrating concepts with a mouse navigating a path and providing practice problems.

Let’s solve each problem step by step.

We are given a rectangle with points A, B, C, D:

- AB = 4m (left side)
- BC = 8m (bottom side)
- CD = 4m (right side)
- DA = 8m (top side)

So it’s a rectangle: 8m long and 4m wide.

Also, we have a compass rose showing directions:
- North is up
- South is down
- East is right
- West is left

Now let’s go through each person’s path.

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Carl walks from point A to point B, to point C, to point D.

Path: A → B → C → D

Distance = total ground covered = AB + BC + CD
= 4m + 8m + 4m = 16 meters

Displacement = how far out of place he is from start to end (straight line from A to D), including direction.

He started at A, ended at D. From A to D is along the top edge — that’s 8m to the East (since D is to the right of A).

So displacement = 8 meters East

✔ Matches what’s written in “I do” section.

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Ted starts at point C, drives to point D, and back to C.

Path: C → D → C

Distance = CD + DC = 4m + 4m = 8 meters

Displacement = he started at C and ended at C → no change in position → 0 meters

✔ Matches what’s written in “We do” section.

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Mike runs from C to D to A, then returns to point D.

Path: C → D → A → D

Let’s break it down:

- C to D = 4m (upward, since C is bottom-right, D is top-right → so this is North)
- D to A = 8m (leftward → West)
- A to D = 8m (rightward → East) ← returning to D

Wait — let’s double-check the path: “from C to D to A, then returns to point D”

So: C → D → A → D

Total distance = CD + DA + AD
But DA and AD are same length: 8m each? Wait — no!

Actually, from D to A is 8m (along top), and from A back to D is also 8m? But that would mean he goes D→A→D, which is 8m + 8m = 16m for just that part.

But let’s list segments:

1. C to D: 4m (North)
2. D to A: 8m (West)
3. A to D: 8m (East) ← because he returns to D

So total distance = 4 + 8 + 8 = 20 meters

Now displacement: where did he start? Point C. Where did he end? Point D.

So straight-line from C to D is 4m upward → which is North

Therefore, displacement = 4 meters North

✔ Matches what’s written in “You do” section.

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All answers provided in the worksheet are correct.

Final Answer:
Carl's distance: 16 meters; Carl's displacement: 8 meters East
Ted's distance: 8 meters; Ted's displacement: 0 meters
Mike's distance: 20 meters; Mike's displacement: 4 meters North