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Lesson 7 of 11
Enlargement using a negative scale factor
I can perform a given enlargement on an object.
Lesson 7 of 11
New
New
Enlargement using a negative scale factor
I can perform a given enlargement on an object.
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.
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.
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.
You could discuss how column vectors and enlarging by a negative scale factor are similar and linked.
Teacher tip
Licence
This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Lesson video
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Prior knowledge starter quiz
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6 Questions
Q1.A transformation is a process that may change the , orientation or position of a shape.
A transformation is a process that may change the , orientation or position of a shape.
Correct Answer: size
size
Q2.Shape B is enlarged to give shape A. What is the scale factor of this enlargement?
Shape B is enlarged to give shape A. What is the scale factor of this enlargement?
$$3$$
$$2$$
$$\frac{1}{2}$$
Correct answer: $$\frac{1}{3}$$
$$\frac{1}{3}$$
$$\frac{1}{9}$$
Q3.Three Oak pupils enlarge the same shape. Whose diagrams are incorrect?
Three Oak pupils enlarge the same shape. Whose diagrams are incorrect?
Correct answer: Aisha's enlargement.
Aisha's enlargement.
Correct answer: Jacobs's enlargement.
Jacobs's enlargement.
Jun's enlargement.
Q4.Shape B is enlarged to give shape A. What is the scale factor of this enlargement?
Shape B is enlarged to give shape A. What is the scale factor of this enlargement?
$$3$$
$$2$$
$$\frac{3}{2}$$
Correct answer: $$\frac{2}{3}$$
$$\frac{2}{3}$$
Q5.Shape B is enlarged to give shape A. The centre of the enlargement is at (-3, ).
Shape B is enlarged to give shape A. The centre of the enlargement is at (-3, ).
Correct Answer: 4, four
4, four
Q6.Describe the transformation that maps shape A onto shape B.
Describe the transformation that maps shape A onto shape B.
An enlargement scale factor $$\frac{1}{2}$$, centre (0,0)
Correct answer: An enlargement scale factor $$\frac{1}{2}$$, centre (-1, -1)
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 $$\frac{1}{2}$$
Assessment exit quiz
Download quiz pdf
6 Questions
Q1.When the scale factor of an enlargement is negative, the image is a rotation of ° of the object.
When the scale factor of an enlargement is negative, the image is a rotation of ° of the object.
Correct Answer: 180
180
Q2.Which diagram shows an enlargement by a negative scale factor?
Which diagram shows an enlargement by a negative scale factor?
Correct Answer: An image in a quiz
Q3.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.
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.
Correct answer: No, a fraction may have an absolute value greater than 1 such as $$\frac{3}{2}$$
No, a fraction may have an absolute value greater than 1 such as $$\frac{3}{2}$$
Q4.Shape A is enlarged to give shape B. The scale factor of this enlargement is .
Shape A is enlarged to give shape B. The scale factor of this enlargement is .
Correct Answer: -2, minus 2, negative 2
-2, minus 2, negative 2
Q5.Shape A is enlarged to give shape B. The centre of enlargement is at the .
Shape A is enlarged to give shape B. The centre of enlargement is at the .
Correct Answer: origin, point (0, 0), (0,0), (0, 0)
origin, point (0, 0), (0,0), (0, 0)
Q6.Shape A is transformed to give shape B. Describe the transformation.
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 $$(0, 0)$$
Correct answer: An enlargement scale factor $$-\frac{5}{2}$$, centre $$(4, 4)$$
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 $$(4, 4)$$