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TRANSFORMATIONS · LESSON 13

Transformations Final Checkpoint

Complete an exam-style assessment across the full topic.

⏱️ 45–58 min 📘 Checkpoint 📍 Coordinate diagrams included

Final Checkpoint

Section A: Core Transformations

  1. Translate A(1,−3) by (−4,6).
  2. Reflect B(5,2) in x=1.
  3. Reflect C(−4,3) in y=−x.
  4. Rotate D(2,−5) 180° about origin.
  5. Enlarge E(4,−2) by scale factor 1/2 about origin.

Section B: Description and Matrices

  1. State the matrix for reflection in y=x.
  2. Apply 01−10 to (3,7) and identify the transformation.
  3. State the complete information needed for an enlargement.
  4. A side grows from 6 cm to 15 cm. Find scale factor.

Section C: Advanced Transformations

  1. Apply 2001 to (−3,4) and name the transformation.
  2. Apply 1−201 to (5,3).
  3. State the invariant line in question 11.
  4. Explain how perpendicular bisectors locate a centre of rotation.

✅ Check Your Work

Show answers and working
  1. A′=(1−4,−3+6)=(−3,3).
  2. B is 4 units right of x=1, so B′=(−3,2).
  3. (x,y)→(−y,−x), so C′=(−3,4).
  4. D′=(−2,5).
  5. E′=(2,−1).
  6. 0110.
  7. Image=(7,−3); 90° clockwise rotation about origin.
  8. Centre of enlargement and scale factor.
  9. 15/6=2.5.
  10. Image=(−6,4); stretch factor 2 in x-direction, invariant y-axis.
  11. x′=5−2(3)=−1, y′=3, so (−1,3). Horizontal shear factor −2.
  12. The x-axis.
  13. The centre lies equally far from each point-image pair, so it lies on each pair’s perpendicular bisector; their intersection gives the centre.

🧠 Learn It Visually: Final Checkpoint Preparation

A strong solution explains the mapping, shows accurate coordinate work and gives a complete description.

Recognise

Identify the likely family of transformation.

Calculate

Use vectors, coordinate rules, distances or matrices.

Verify

Check orientation, size, invariant features and correspondence.

🎯 Identify the Transformation

Study the object and image, then choose the most complete description.

ObjectImage
Look at size, orientation and corresponding movements.
Think Like a Mathematician: How would you prove that a transformation description is correct rather than merely plausible?

🧷 Remember

Object → image, not image → object, unless the question explicitly asks for the inverse transformation.

⚠️ Common Mistake

Using an accurate diagram as a substitute for calculation or explanation.

🎯 Exam Tip

Write the full transformation description as your final line and check every required parameter.

Revision Guidance and Readiness