Let's solve the problem step by step.
---
Problem:
Jude walks:
- 5 miles
north
- 1 mile
east
- 7 miles
south
- 1 mile
west
He wants to get back home. We need to find:
- The
direction he must take to return to his starting point (home).
- We’ll use a graph to trace his path and determine the final displacement.
---
Step 1: Set Up a Coordinate System
We’ll use a coordinate grid where:
- The
starting point (home) is at the origin:
(0, 0)
- North = positive y-direction
- South = negative y-direction
- East = positive x-direction
- West = negative x-direction
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Step 2: Track Jude’s Movement
Start at:
(0, 0)
1.
5 miles north → Add 5 to y
→ New position:
(0, 5)
2.
1 mile east → Add 1 to x
→ New position:
(1, 5)
3.
7 miles south → Subtract 7 from y
→ New position:
(1, 5 - 7) = (1, -2)
4.
1 mile west → Subtract 1 from x
→ New position:
(1 - 1, -2) = (0, -2)
So, after all his walking, Jude is at
(0, -2)
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Step 3: Determine How to Get Back Home
Home is at
(0, 0)
Jude is at
(0, -2)
To get back:
- He needs to move
2 miles north (since he is 2 units below the origin on the y-axis)
There is no change in x-direction (he’s already at x = 0).
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✔ Answer:
Jude must walk
2 miles north to get back home.
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Graph Explanation (How to draw it):
On the grid:
1. Start at
(0, 0) — mark this as "home".
2. Move up 5 units → (0, 5)
3. Move right 1 unit → (1, 5)
4. Move down 7 units → (1, -2)
5. Move left 1 unit → (0, -2)
Now, draw an arrow from
(0, -2) back to
(0, 0) — this is
2 miles north.
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📌 Final Answer:
Jude must walk 2 miles north to get back home.
✔ You can now draw the path on the grid accordingly.
Parent Tip: Review the logic above to help your child master the concept of multi step word problems 6th grade worksheet.
