This worksheet introduces transformations on the Cartesian plane, teaching students to find the coordinates of a shape's image after a translation, reflection or rotation. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A translation slides a point by adding/subtracting fixed amounts to its x- and y-coordinates: (x,y) → (x+a, y+b).
- Reflecting across the x-axis flips the sign of y: (x,y) → (x,−y). Reflecting across the y-axis flips the sign of x: (x,y) → (−x,y).
- Rotating 180° about the origin flips the sign of both coordinates: (x,y) → (−x,−y).
- Rotating 90° anticlockwise about the origin: (x,y) → (−y,x). Rotating 90° clockwise: (x,y) → (y,−x).
- A shape's vertices can each be transformed individually using the same rule, to find the whole image shape.
What your child will practise:
- Applying a translation rule to a point's coordinates by adding/subtracting the given amounts.
- Applying a reflection rule (across the x-axis or y-axis) by flipping the sign of the correct coordinate.
- Applying a rotation rule about the origin using the correct coordinate swap/sign pattern for 90°, 180°, or 270°.
- Transforming every vertex of a shape using the same rule to find the coordinates of the whole image.
- Applying two transformations in sequence, using the result of the first as the input to the second.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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