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Rotations (OCR GCSE Maths)
Revision Note
Rotations
What is a rotation?
- A rotation is the movement of an object around a point
- The rotated image is the same size and shape as the original image, but it will have a new position and orientation
How do I rotate a shape?
- You need to be able to perform a rotation (on a coordinate grid)
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The easiest way to draw a rotation is to use tracing paper, this should be available to you in an exam but you may have to ask an invigilator for it
- STEP 1:
Place the tracing paper over page and draw over the original object
- STEP 2:
Place the point of your pencil on the centre of rotation
- STEP 3:
Rotate the tracing paper the angle that has been asked for in the question, it will usually be an "easy" angle such as 90o, 180o or 270o
- STEP 4:
Your tracing paper is in the position showing you where to draw the rotated image, carefully draw the image onto the coordinate grid
How do I describe a rotation?
- You will need to be able to identify and describe a rotation when presented with one
- You must fully describe a transformation to get full marks
- For a rotation you must:
- State that the transformation is a rotation
- State the centre of rotation (the point about which the object is rotated)
- State the angle of rotation (how many degrees around the point that the object has been rotated)
- State the direction of rotation (clockwise or anticlockwise, unless the angle is 180o, then a direction is not required)
Which points are invariant with a rotation?
- Invariant points are points that do not change position when a transformation has been performed
- Invariant points don't move!
- With a rotation, if the centre of rotation is a point on the object, then that point is invariant
- if the centre of rotation is not a point on the object, then there are no invariant points
- Rotating an object by 360° (or any multiple of 360) means it returns back to its original position
- all points on the object are invariant in this case
- be careful: rotating a rectangle by 180° about its centre might look like the rectangle hasn't changed, but individual points have moved position (so they're not invariant)
Examiner Tip
- Draw an arrow facing “up” on your tracing paper, as you rotate it, it’ll be really easy to see when you’ve turned 90° (arrow will be facing left or right), 180° (arrow facing down) etc.
- Make sure that you double check that you have copied the rotated image into the correct position by putting the tracing paper over the original object and rotating it again to see that it lines up with your image
Worked example
(a)
On the grid below rotate shape A by 90o anti-clockwise about the point (0, 2).
Label your answer A'.
Using tracing paper, draw over the original object and mark one vertex.
Mark on the centre of rotation.
Draw an arrow pointing vertically upwards on the paper.
With your pencil fixed on the point of rotation, rotate the tracing paper 90o anti-clockwise, the arrow that you drew should now be pointing left.
Make a mental note of the new coordinates of the vertex that you marked on your tracing paper.
Draw the new position of this vertex onto the grid.
Repeat this process for the other two vertices on the triangle.
Connect the vertices together to draw the rotated image.
(b)
Describe fully the single transformation that creates shape B from shape A.
You should be able to see that the object has been rotated 90o clockwise (or 270o anti-clockwise).
You are likely to be able to see roughly where the centre of rotation is but it may take a little time to find its position exactly.
To find the exact coordinates of the centre of rotation you can play around with tracing paper.
Draw over shape A on tracing paper, then try out different locations for the centre of rotation by placing your pencil on a point, rotating the paper 90o clockwise and seeing if it lines up with shape B.
Write down the all of the elements required to fully describe the transformation: the type of transformation, the centre of rotation, the angle and the direction.
Rotation, 90o clockwise with centre (-4, 0)
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