What Is a Rotations Chart?
A rotations chart is a visual tool that helps you see how a shape moves when it is rotated around a point on the coordinate plane. It lists the coordinates of the original points, the angle of rotation, and the new coordinates after the rotation. For GCSE Maths students, this chart simplifies the process of solving rotation problems and checking your answers quickly.
Why Use a Rotations Chart in GCSE Maths?
Rotating a shape is a common question in the Coordinate Geometry unit. A rotations chart gives you:
- A systematic way to record each step.
- Immediate verification of the final coordinates.
- Clear visual feedback, which is especially helpful for visual learners.
- A reference you can bring to exams, making the process faster and less error‑prone.
Creating a Rotations Chart
Follow these simple steps to build your own chart:
- List the original points. Write the coordinates of every vertex of the shape in the first column.
- Choose the rotation centre. Most GCSE questions use the origin (0, 0). If a different point is given, note it in the heading.
- Select the rotation angle. Common angles are 90°, 180°, and 270°. Write this in a second column.
- Apply the rotation formulas. For a rotation about the origin:
- 90° clockwise: (x, y) → (y, –x)
- 180°: (x, y) → (–x, –y)
- 270° clockwise: (x, y) → (–y, x)
- Record the new coordinates. Fill in a third column with the results.
- Check your work. Verify that the new points maintain the shape’s size and orientation.
Common Rotation Angles and Their Effects
Understanding how each angle transforms coordinates is key:
- 90° clockwise swaps the x and y values and flips the new x to negative.
- 180° simply reverses both coordinates.
- 270° clockwise (or 90° counter‑clockwise) flips the new y to negative and swaps the coordinates.
When rotating counter‑clockwise, reverse the signs accordingly. Practice both directions to build flexibility.
Example 1: Rotating a Triangle
Rotate triangle ABC with vertices A(2, 3), B(5, 1), and C(4, 4) about the origin by 90° clockwise.
Using the chart:
Original PointRotationNew Point A(2,
