Describing a negative enlargement | Maths | Quizalize & Oak National Academy

Starter quiz

When the scale factor of an enlargement is negative, the image is a ______ of 180° of the object.

'rotation' ✓
Which diagram shows an enlargement by a positive scale factor?
Sam enlarges a shape. The image is smaller than the object and the orientation is different. Which of these statements is correct?

Sam's scale factor is less than -1

Sam's scale factor is greater than -1

Sam's scale factor is between -1 and 1

Sam's scale factor is between 0 and 1

Sam's scale factor is between -1 and 0 ✓
Shape A is enlarged by the scale factor $-\frac{1}{3}$ to give shape B. The scale factor that would map shape B back onto shape A is ______.

'-3' ✓
Shape B is enlarged to give shape A. What is the scale factor of the enlargement?

$2$

$\frac{1}{2}$

$-\frac{1}{2}$ ✓

$-2$
Shape A is transformed to give shape A. Describe the transformation fully.

An enlargement scale factor -0.5

An enlargement scale factor -2

An enlargement scale factor -3 ✓

centre (3, 3) ✓

centre (4, 4)

Exit quiz

An enlargement will produce an image that is ______ to the object.

'similar' ✓
Shape A is enlarged to give shape B. Shape B is smaller than shape A. This means that the scale factor is __________.

equal to -1

equal to 1

greater than -1

less than 1

between -1 and 1 ✓
Which of these show an enlargement with a negative scale factor?
Shape A is enlarged to give shape B. The scale factor of this enlargement is ______.

'-2' ✓
Shape A is enlarged to give shape B. Describe the transformation.

An enlargement scale factor $2$ , centre $(3, 2)$

An enlargement scale factor $\frac{1}{2}$ , centre $(2, 3)$ ✓

An enlargement scale factor $-2$ , centre $(2, 3)$

An enlargement scale factor $-\frac{1}{2}$ , centre $(2, 3)$

An enlargement scale factor $\frac{1}{2}$ , centre $(3, 2)$
Shape A is transformed to give shape B. Describe the transformation.

An enlargement scale factor $2$ , centre $(1, 2)$

An enlargement scale factor $\frac{1}{2}$ , centre $(0, 2)$

An enlargement scale factor $-2$ , centre $(0, 2)$

An enlargement scale factor $-2$ , centre $(1, 2)$ ✓

An enlargement scale factor $-\frac{1}{2}$ , centre $(1, 2)$

Worksheet

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Lesson Details

Key learning points

If the image is the opposite side of the centre of enlargement and rotated 180°, there is a negative scale factor.
If the image has changed size, there has been an enlargement with scale factor ≠ 1.
To describe an enlargement, you must state the centre of enlargement and the scale factor.

Common misconception

Pupils may want to write the transformation as two transformations, a rotation of 180° followed by an enlargement by a positive scale factor, rather than a single transformation.

Remind pupils that a single transformation is more efficient than multiple transformations.

Keywords

Transformation - A transformation is a process that may change the size, orientation or position of a shape.
Enlargement - Enlargement is a transformation that causes a change of size.
Scale factor - A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.
Centre of enlargement - The centre of enlargement is the point from which a shape is enlarged.
Absolute value - The absolute value of a number is its distance from zero.