Problem solving with transformations | Maths | Quizalize & Oak National Academy

Starter quiz

The ______ is the distance around a 2D shape.
- 'perimeter' ✓
Match the inverse operations.
- $+$
  
  ⇔
  
  $-$ ✓
- $\times$
  
  ⇔
  
  $\div$ ✓
- $-$
  
  ⇔
  
  $+$ ✓
- $\div$
  
  ⇔
  
  $\times$ ✓
Complete the descriptions below by matching the transformation with the detail needed to describe it fully.
- A rotation
  
  ⇔
  
  by ${90^{\circ}}$ clockwise about (3,4) ✓
- A reflection
  
  ⇔
  
  in the y-axis. ✓
- A translation
  
  ⇔
  
  by ${-1 \choose 5}$ ✓
- An enlargement
  
  ⇔
  
  by scale factor 0.25 from (0, 0) ✓
What is the area of a triangle with a base length of 6 cm and perpendicular height of 8 cm?
- 48 cm ${^{2}}$
- 24 cm ${^{2}}$ ✓
- 48 cm
- 24 cm
Which transformation does this property table belong to?
- translation
- rotation
- reflection
- enlargement ✓
The point (3, 5) is reflected in the ______-axis to become (-3, 5).
- 'y' ✓

The perimeter and area are the same after a translation, rotation or reflection because the object and image are ______.
- 'congruent' ✓
A shape is rotated ${90^{\circ}}$ anti-clockwise about $(2,7)$ . Which of the following rotations would result in the image being moved to the same position as the original object?
- Rotation ${90^{\circ}}$ clockwise about $(2,7)$ ✓
- Rotation ${90^{\circ}}$ clockwise about $(7,2)$
- Rotation ${270^{\circ}}$ anti-clockwise about $(2,7)$ ✓
The coordinate $(a, b)$ has been translated by ${4 \choose 3}$ . The image of this point will have the coordinate __________.
- $(4a, 3b)$
- $(a4, b3)$
- $(a + 4, b + 3)$ ✓
- $(a - 4, b - 3)$
Shape A is reflected in the $x$ -axis to create shape B. Shape B is then reflected in the $y$ -axis to create shape C. Which transformations would map shape C onto shape A?
- A rotation ${180^{\circ}}$ about the origin. ✓
- A reflection in the line that passes through $(-4, 4)$ and $(3, -3)$ ✓
- A translation by ${4 \choose 4}$
- A reflection in the line that passes through (4, 4) and (-2, -2)
A shape with perimeter 16 cm is enlarged by scale factor 3. The perimeter of the image is ______ cm.
- '48 cm' ✓
The point A(p + 3, q + 5) has the image $A^{\prime}$ (p + 1, q + 8). Which vector has it been translated by?
- ${2 \choose 3}$
- ${-2 \choose 3}$ ✓
- ${2 \choose -3}$
- ${-2p \choose 3q}$

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By understanding what changes and what is invariant, you can determine whether a transformation has occurred.
Sometimes you might need to persevere in order to find the right transformation.
You may be able to check your deductions by carrying out the transformation.

When completing an inverse translation, students may believe they need to flip the vector.

Ask students to say in words how you would return to the starting point, to highlight the direction needed and then link to the vector.

Transformation - A transformation is a process that may change the size, orientation or position of a shape.
Object - The object is the starting figure, before a transformation has been applied.
Image - The image is the resulting figure, after a transformation has been applied.