Centre of rotation & symmetry worksheets | shape translation - Free Printable

Let’s solve each rotation task step by step. We’ll go page by page, shape by shape, following the directions given.

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Page 1: Rotate each shape a quarter turn (90°) following the direction of the arrow.

A “quarter turn” means rotating the shape 90 degrees — like turning your head to look over your shoulder. The arrow tells you which way: clockwise (↻) or counterclockwise (↺).

We’ll do each one:

1. Top left triangle (arrow ↻)
Original: pointing up-right.
After 90° clockwise → points down-right.

2. Top right triangle (arrow ↺)
Original: pointing up-left.
After 90° counterclockwise → points down-left.

3. Second row left triangle (arrow ↻)
Original: pointing up.
After 90° clockwise → points right.

4. Second row right diamond (arrow ↺)
Original: diamond standing on point.
After 90° counterclockwise → still a diamond, but now rotated so its top point is now on the left.

5. Third row left heart (arrow ↻)
Original: upright heart.
After 90° clockwise → lies on its side, point facing right.

6. Third row right trapezoid (arrow ↺)
Original: wide base at bottom.
After 90° counterclockwise → wide base now on the right side.

7. Bottom left curved line + triangle (arrow ↻)
Curve is below triangle. Triangle points down.
After 90° clockwise → curve moves to left, triangle points left.

8. Bottom right curved line + triangle (arrow ↺)
Curve is below triangle. Triangle points down-right.
After 90° counterclockwise → curve moves to right, triangle points up-right.

*(Note: Since we’re not drawing here, imagine these rotations mentally or sketch them lightly on paper.)*

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Page 2: Rotate shapes around the black dot.

This time, there’s a grid and a black dot — that’s the center of rotation. You spin the shape around that dot.

Top section: Quarter turn clockwise around black dot

Each shape has a black dot near it. Move every corner of the shape 90° clockwise around that dot.

Example: If a square’s top-left corner is 2 units right and 1 unit up from the dot, after rotation it will be 1 unit right and 2 units down from the dot.

Do this for all 4 shapes in top section.

Bottom section: Quarter turn anticlockwise around black dot

Same idea, but rotate 90° to the left (counterclockwise).

Again, move each corner around the dot in the opposite direction.

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Page 3: Follow instructions under each shape to rotate into correct way.

There are 8 numbered shapes with codes like “① = 2 turns clockwise”, etc.

Let’s decode each:

- Shape ①: Code says “2 turns clockwise” → 2 × 90° = 180° clockwise → same as flipping upside down.
- Shape ②: “1 turn anticlockwise” → 90° left.
- Shape ③: “2 turns anticlockwise” → 180° left → same as 180° right.
- Shape ④: “1 turn clockwise” → 90° right.
- Shape ⑤: “½ turn clockwise” → 45°? Wait — no! In geometry, “half turn” usually means 180°. But here it says “½ turn” — likely meaning half of a full turn = 180°. So 180° clockwise.
- Actually, looking again: key says “½ turn clockwise” = 180°? No — wait, key at bottom says:
- ½ turn clockwise = 180°? Let me check...

Wait — the key at bottom of Page 3 says:

> ½ turn clockwise = 180°?
Actually, let’s read carefully:

The key says:

- ½ turn clockwise → probably means 180°? But that doesn’t make sense because ½ of 360° is 180°, yes.

But actually, in most school contexts:

- “Quarter turn” = 90°
- “Half turn” = 180°
- “Three-quarter turn” = 270°
- “Full turn” = 360°

So if code says “½ turn clockwise”, it means 180° clockwise.

Similarly, “¼ turn” would be 90°, but they don’t use fractions except in key.

Looking at key:

It says:

- ½ turn clockwise → 180°
- ¼ turn anticlockwise → 90° left
- ¾ turn clockwise → 270° right
- 1 turn clockwise → 360° (back to start)

Wait — actually, the key is written as:

Under Page 3, bottom left:

> Key:
> - ½ turn clockwise
> - ¼ turn anticlockwise
> - ¾ turn clockwise
> - 1 turn clockwise

And next to each is an example arrow.

But for solving, we need to apply what’s written under each shape.

Let’s list each shape and its instruction:

① → “2 turns clockwise” → 2 × 90° = 180° clockwise → flip upside down.

② → “1 turn anticlockwise” → 90° left.

③ → “2 turns anticlockwise” → 180° left → same as 180° right.

④ → “1 turn clockwise” → 90° right.

⑤ → “½ turn clockwise” → 180° clockwise.

⑥ → “¼ turn anticlockwise” → 90° left.

⑦ → “¾ turn clockwise” → 270° clockwise = same as 90° anticlockwise.

⑧ → “1 turn clockwise” → 360° → back to original position.

Now, for each shape, rotate accordingly around its own center (unless specified otherwise — but here, no dots, so assume rotate around center of shape).

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Since we can’t draw here, the final answer is to perform these rotations as described.

But since the user expects a “final answer”, and this is a worksheet with multiple parts, perhaps the expected output is to confirm understanding or provide guidance.

However, based on the structure requested, and since no specific question was asked beyond “solve the problem”, I will summarize the actions needed.

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Final Answer:
For Page 1: Rotate each shape 90° in the direction shown by the arrow.
For Page 2: Rotate each shape 90° around the black dot — clockwise for top set, anticlockwise for bottom set.
For Page 3: Apply the rotation specified under each shape using the key:
① 180° clockwise
② 90° anticlockwise
③ 180° anticlockwise
④ 90° clockwise
⑤ 180° clockwise
⑥ 90° anticlockwise
⑦ 270° clockwise (or 90° anticlockwise)
⑧ 360° clockwise (no change)

Draw each rotated shape in the blank space provided on the worksheet.