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Cartesian Plane Rotations

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Cartesian Plane Rotations

Cartesian plane with rotation arrows

🎯 WALT (We Are Learning To)

Today we are learning to:

• Describe rotations of points on the Cartesian plane around a given point using degrees and direction

• Understand the effect of rotation transformations on coordinates

• Communicate and justify the steps involved in rotating simple shapes

📚 Part 1: Understanding Rotations

1. When we rotate point (3, 2) by 90° clockwise around the origin, what happens to the coordinates?

(2, -3)

(-2, 3)

(3, -2)

(-3, 2)

2. Which direction means turning the same way as clock hands move?

Clockwise

Anticlockwise

3. When a point is rotated 180° around the origin, what happens to both coordinates?

They both change sign (positive becomes negative, negative becomes positive)

They both stay the same

Only the x-coordinate changes sign

They swap positions

4. Check all the rotation amounts that would bring a point back to its starting position:

360°

180°

720°

90°

✏️ Part 2: Applying Rotations

5. Complete the rotation: Point A(4, 1) rotated 90° anticlockwise around the origin becomes A'(_____, _____)
6. Point B(-2, 3) is rotated 270° clockwise around the origin. What are the new coordinates?

New coordinates: B'(_____, _____)

7. Explain in your own words what happens to the coordinates when you rotate a point 180° around the origin:
8. Draw and label the following on the coordinate grid below:

• Original point P(2, -1)

• P' after 90° clockwise rotation around origin

• P'' after 180° rotation from the original point

🌟 Success Criteria Check

Tick each box when you can do it confidently:

I can define rotation in degrees around a point on the Cartesian plane

I can rotate a point 90°, 180°, and 270° clockwise and anticlockwise

I can describe the change to coordinates after a rotation

I can explain my reasoning to a peer in a group discussion

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