New
New
Year 7

# Problem solving with transformations

I can use my knowledge of transformations to solve problems.

New
New
Year 7

# Problem solving with transformations

I can use my knowledge of transformations to solve problems.

## Lesson details

### Key learning points

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

### Common misconception

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.

### Keywords

• 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.

This lessons draws on perimeter and area, coordinates and algebra, so you may need to support or add extra examples.
Teacher tip

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

### 6 Questions

Q1.
The is the distance around a 2D shape.
Q2.
Match the inverse operations.
Correct Answer:$$+$$,$$-$$

$$-$$

Correct Answer:$$\times$$,$$\div$$

$$\div$$

Correct Answer:$$-$$,$$+$$

$$+$$

Correct Answer:$$\div$$,$$\times$$

$$\times$$

Q3.
Complete the descriptions below by matching the transformation with the detail needed to describe it fully.
Correct Answer:A rotation ,by $${90^{\circ}}$$ clockwise about (3,4)

by $${90^{\circ}}$$ clockwise about (3,4)

in the y-axis.

Correct Answer:A translation,by $${-1 \choose 5}$$

by $${-1 \choose 5}$$

Correct Answer:An enlargement,by scale factor 0.25 from (0, 0)

by scale factor 0.25 from (0, 0)

Q4.
What is the area of a triangle with a base length of 6 cm and perpendicular height of 8 cm?
48 cm$${^{2}}$$
Correct answer: 24 cm$${^{2}}$$
48 cm
24 cm
Q5.
Which transformation does this property table belong to?
translation
rotation
reflection
Q6.
The point (3, 5) is reflected in the -axis to become (-3, 5).

## Exit quiz

### 6 Questions

Q1.
The perimeter and area are the same after a translation, rotation or reflection because the object and image are .
Q2.
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?
Correct answer: Rotation $${90^{\circ}}$$ clockwise about $$(2,7)$$
Rotation $${90^{\circ}}$$ clockwise about $$(7,2)$$
Correct answer: Rotation $${270^{\circ}}$$ anti-clockwise about $$(2,7)$$
Q3.
The coordinate $$(a, b)$$ has been translated by $${4 \choose 3}$$. The image of this point will have the coordinate __________.
$$(4a, 3b)$$
$$(a4, b3)$$
Correct answer: $$(a + 4, b + 3)$$
$$(a - 4, b - 3)$$
Q4.
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?
Correct answer: A rotation $${180^{\circ}}$$ about the origin.
Correct answer: 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)
Q5.
A shape with perimeter 16 cm is enlarged by scale factor 3. The perimeter of the image is cm.
Correct Answer: 48 cm, 48cm, 48
Q6.
The point A(p + 3, q + 5) has the image $$A^{\prime}$$(p + 1, q + 8). Which vector has it been translated by?
$${2 \choose 3}$$
Correct answer: $${-2 \choose 3}$$
$${2 \choose -3}$$
$${-2p \choose 3q}$$