Translating Shapes - Maths with Mum - Free Printable

Let's solve the "Translating Shapes" problem step by step. The task is to translate (slide) each shape on the grid according to the given instructions.

We'll go through each part (a) through (f), and determine where the shape should be moved based on the directions.

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Understanding Translations

- Left/Right: Move horizontally.
- Left = subtract from x-coordinate
- Right = add to x-coordinate
- Up/Down: Move vertically.
- Up = add to y-coordinate
- Down = subtract from y-coordinate

We’ll use a coordinate system where:
- The bottom-left corner of the grid is (0, 0)
- Moving right increases the x-value
- Moving up increases the y-value

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Part (a): 4 places left

Original shape: A small square located at the top-right of its grid.
Let’s find the coordinates of the square:
- It appears to be a 1x1 square with bottom-left corner at (7, 6)

Now move 4 places left → subtract 4 from x-coordinate:
- New x = 7 - 4 = 3
- So new position: (3, 6)

✔ Draw a square at (3, 6)

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Part (b): 3 places up, 5 places left

Original shape: A small square at (8, 4)

Move:
- 5 places left → x = 8 - 5 = 3
- 3 places up → y = 4 + 3 = 7

New position: (3, 7)

✔ Draw a square at (3, 7)

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Part (c): 4 places right, 4 places up

Original shape: A square at (4, 4)

Move:
- 4 right → x = 4 + 4 = 8
- 4 up → y = 4 + 4 = 8

New position: (8, 8)

✔ Draw a square at (8, 8)

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Part (d): 6 places up, 3 places right

Original shape: A vertical rectangle (or tall bar) at (2, 2) to (2, 4) — it's 3 units high.

We translate every point:
- Bottom point: (2, 2)
- Top point: (2, 4)

Move:
- 3 right → x = 2 + 3 = 5
- 6 up → y = 2 + 6 = 8 for bottom; 4 + 6 = 10 for top

So new points: (5, 8) to (5, 10)

✔ Draw a vertical bar from (5, 8) to (5, 10)

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Part (e): 1 place right, 3 places down

Original shape: A triangle at (2, 5), with base from (2, 5) to (3, 5) and tip at (2.5, 6)

But since we're working on a grid, let's assume it's made of grid points.

The triangle has:
- Base: (2, 5) and (3, 5)
- Apex: (2.5, 6) — but since it's on a grid, likely centered between (2,6) and (3,6), so apex at (2.5,6) or just approximate as three points.

But simpler: treat it as a triangle with vertices at:
- (2, 5)
- (3, 5)
- (2.5, 6)

Now move:
- 1 right → x += 1
- 3 down → y -= 3

New vertices:
- (2+1, 5-3) = (3, 2)
- (3+1, 5-3) = (4, 2)
- (2.5+1, 6-3) = (3.5, 3)

So new triangle: base from (3,2) to (4,2), apex at (3.5,3)

✔ Draw this triangle

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Part (f): 6 places up, 2 places right

Original shape: A right triangle with:
- Points: (3, 3), (5, 3), (3, 5)

This is a right triangle with legs along the axes.

Now move:
- 2 right → x += 2
- 6 up → y += 6

New points:
- (3+2, 3+6) = (5, 9)
- (5+2, 3+6) = (7, 9)
- (3+2, 5+6) = (5, 11)

So new triangle: (5,9), (7,9), (5,11)

✔ Draw this triangle

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✔ Summary of Final Positions:

| Part | Original Shape | Movement | New Position |
|------|----------------|----------|--------------|
| (a) | Square at (7,6) | 4 left | (3,6) |
| (b) | Square at (8,4) | 3 up, 5 left | (3,7) |
| (c) | Square at (4,4) | 4 right, 4 up | (8,8) |
| (d) | Rectangle from (2,2) to (2,4) | 3 right, 6 up | (5,8) to (5,10) |
| (e) | Triangle: (2,5), (3,5), (2.5,6) | 1 right, 3 down | (3,2), (4,2), (3.5,3) |
| (f) | Triangle: (3,3), (5,3), (3,5) | 2 right, 6 up | (5,9), (7,9), (5,11) |

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🔍 How to Complete the Worksheet:

On your printed copy:
1. For each part, locate the original shape.
2. Apply the translation (move the shape accordingly).
3. Draw the translated shape in the new location.

Make sure the shape stays the same size and orientation — only its position changes.

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Let me know if you'd like a visual sketch or help drawing it!