Enlargement using a negative scale factor | Maths | Quizalize & Oak National Academy

Starter quiz

A transformation is a process that may change the ______, orientation or position of a shape.

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

$3$

$2$

$\frac{1}{2}$

$\frac{1}{3}$ ✓

$\frac{1}{9}$
Three Oak pupils enlarge the same shape. Whose diagrams are incorrect?

Aisha's enlargement. ✓

Jacobs's enlargement. ✓

Jun's enlargement.
Shape B is enlarged to give shape A. What is the scale factor of this enlargement?

$3$

$2$

$\frac{3}{2}$

$\frac{2}{3}$ ✓
Shape B is enlarged to give shape A. The centre of the enlargement is at (-3, ______).

'4' ✓
Describe the transformation that maps shape A onto shape B.

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

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

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

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

An enlargement scale factor $\frac{1}{2}$

Exit quiz

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

'180' ✓
Which diagram shows an enlargement by a negative scale factor?
Laura says, "When you enlarge an object by a fractional scale factor, the image is always smaller than the object." Is Laura correct? Justify your answer.

Yes, any enlargement by a scale factor less than 1 gives a smaller image.

No, the scale factor could be negative so the image will be larger.

No, a fraction may have an absolute value greater than 1 such as $\frac{3}{2}$ ✓
Shape A is enlarged to give shape B. The scale factor of this enlargement is ______.

'-2' ✓
Shape A is enlarged to give shape B. The centre of enlargement is at the ______.

'origin' ✓
Shape A is transformed to give shape B. Describe the transformation.

An enlargement scale factor $\frac{3}{2}$ , centre $(4, 4)$

An enlargement scale factor $-\frac{3}{2}$ , centre $(0, 0)$

An enlargement scale factor $-\frac{5}{2}$ , centre $(4, 4)$ ✓

An enlargement scale factor $-\frac{5}{2}$ , centre $(0, 0)$

An enlargement scale factor $\frac{5}{2}$ , centre $(4, 4)$

Worksheet

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Lesson Details

Key learning points

Each length in the shape is multiplied by the scale factor.
Each vertex in the object is a given distance from the centre of enlargement.
This distance is also multiplied by the scale factor to give the distance of the image's vertex.
A negative scale factor produces an image that is the other side of centre of enlargement.
To enlarge, you need the centre of enlargement and a scale factor.

Common misconception

Pupils may think that a negative scale factor creates a smaller image than the object.

Remind them that the absolute value will be less than 1 and greater than 0 to create a smaller image. Whether the scale factor is positive or negative does not affect this.

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.