Same orientation and size
Often a translation or rotation.
Mixed Review
- Translate (−2,4) by (5,−3).
- Reflect (3,−7) in the x-axis.
- Reflect (−2,5) in y=x.
- Rotate (4,1) 90° anticlockwise about origin.
- Enlarge (−3,2) by scale factor −2 about origin.
- Identify matrix −1001.
- Apply 0−110 to (2,6).
- Apply horizontal shear factor 3 to (1,2).
- State the invariant line of an x-direction stretch.
- Explain why a rotation description needs three pieces of information.
✅ Check Your Work
Show answers and working
- (3,1).
- (3,7).
- (5,−2).
- (−1,4).
- (6,−4).
- Reflection in the y-axis.
- (−6,2), a 90° anticlockwise rotation.
- (1+3×2,2)=(7,2).
- The y-axis.
- Centre, angle and direction are all required to determine one unique rotation.
🧠 Learn It Visually: Mixed Review Strategy
Mixed questions test recognition before calculation. Start by comparing size, orientation, parallelism and distances.
Reversed orientation
Often a reflection or a transformation involving a negative determinant.
Changed size or shape
Consider enlargement, stretch or shear.
🎯 Identify the Transformation
Study the object and image, then choose the most complete description.
Look at size, orientation and corresponding movements.
Think Like a Mathematician: What is the smallest set of clues needed to distinguish translation, reflection and rotation?
🧷 Remember
Recognition is only the first step; your final description must be complete.
⚠️ Common Mistake
Naming the type correctly but omitting the vector, line, centre, angle or factor.
🎯 Exam Tip
Use one pair of corresponding vertices to test your suspected rule before committing.
Revision Guidance and Readiness
- Attempt the questions without notes first.
- Use the answers or worked solutions to identify the exact step that needs attention.
- Return to the relevant lesson, then retry missed questions.
- You are ready to move on when you can explain your method and check your result independently.