Dilation and Similarity Year 8

Dilation and Similarity

By Kate Marshall

​Dilations

A dilation is a transformation that alters the SIZE of an object, but NOT the shape nor the orientation.

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Scale factor (k)

Reduction

​

0<k < 1

Enlargement

.

k > 1

Multiple Choice

When a figure is dilated, its shape is altered.

• True

• False

Multiple Choice

What is the symbol used for scale factor?

• D

• DF

• k

• $$\psi$$

Multiple Choice

If the scale factor is between 0 and 1, then the image produced will be:

• an enlargement

• the same size

• a reduction

• Not enough information to decide

Multiple Choice

Which of the labelled sides in this right angled triangle is the HYPOTENUSE?

• P

• Q

• R

Multiple Choice

The triangle shown is dilated by a factor k=4. What will be the length of the HYPOTENUSE?

• 20

• 16

• 14

• 28

​SIMILAR SHAPES

​Two shapes are said to be similar if they have the same shape. (They DO NOT need to have the same size).

A scale factor k=2 has been used to enlarge the original quadrilateral.
The corresponding sides in the image are double those in the original.

Multiple Choice

The pink triangle is the original. What scale factor was used to produce the blue triangle?

• $$1$$

• $$\frac{1}{3}$$

• $$2$$

• $$3$$

Multiple Choice

Congruent shapes are also similar.

• True

• False

Multiple Choice

Similar shapes are also congruent

• True

• False

Multiple Choice

What scale factor will produce an image which is congruent to the original?

• $$k=1$$

• $$k=0$$

• $$k=10$$

• $$k=\frac{1}{10}$$

Multiple Choice

The two quadrilaterals shown are similar. Which side in the smaller quadrilateral corresponds to side NM in the larger?

• Side QP

• Side RS

• Side PS

• Side RQ

Multiple Choice

What is the value of x (the length of side QP) ?

• 10 cm

• 5 cm

• 3 cm

• 7.5 cm

Multiple Choice

These two shapes are similar.

What scale factor was used to create the image from the original?

• $$4$$

• $$2.666...$$

• $$0.375$$

• $$\frac{1}{4}$$