Geometric Transformations

Question 1

Translations can be described in what three ways?

Answer 1

In words
As an algebraic rule
As a vector

Question 2

Rotations are described by what three things?

Answer 2

Centre of rotation
Direction of rotation (clockwise or counter-clockwise / anti-clockwise)
Angle of rotation

Question 3

Reflections are described by the ____

Answer 3

Line of reflection

Question 4

Dilations / enlargements on a coordinate plane are described by the

Answer 4

Centre point

Scale factor

Question 5

Dilations can make a shape bigger or smaller. What are the mathematical terms for this?

Answer 5

Expansion / enlargement and contraction / reduction

Question 6

A dilation is an expansion / enlargement if its scale factor is

Answer 6

Greater than 1

Question 7

A dilation is a contraction if its scale factor is

Answer 7

Between 0 and 1

Question 8

A dilation of scale factor 1 would ____

Answer 8

not change the object.

Question 9

A transformation transforms a shape from a(n) ____ to an ____

Answer 9

from an object / pre-image to an image

Question 10

If a point P is reflected to point P’, then the mirror line would be the ____ ____ of the line segment PP’ (the line between P and P’)

Answer 10

perpendicular bisector

Question 11

Will a fractional scale factor always make the image of a dilation smaller than the object?

Answer 11

No, the fraction could be greater than 1, which would be an expansion / enlargement of the object.

Question 12

What stays the same and what changes when a shape is dilated?

Answer 12

The angles stay the same
The relative sizes of side lengths stays the same (they are in the same ratio, proportion)

The absolute size of side lengths changes (the actual size)

The object and the image are SIMILAR, but not CONGRUENT

(unless it’s scale factor 1, then it’s usually said to be both similar and congruent)

Question 13

When a plane figure (2D shape) is dilated by scale factor 2, what happens to the side lengths and what happens to the area?

Answer 13

The side lengths double (x2)

The area quadruples (x2 squared, or x4)

Question 14

When a plane figure (2D shape) is dilated by a scale factor of 3, what happens to the side lengths and what happens to the area?

Answer 14

The side lengths triple (x3)
The area nonuples (x3 squared, or x9)

Refer to https://en.wikipedia.org/wiki/Tuple for a list of “-ples”

Question 15

What stays the same and what changes when a shape is rotated?

Answer 15

Same proportions
Same angles
Same size
Same orientation

The object and the image are congruent (and also similar)

Question 16

What stays the same and what changes in a reflection?

Answer 16

Same proportions
Same angles
Same size
Different orientation

The object and the image are congruent and similar.

Question 17

What stays the same and what changes in a translation?

Answer 17

Same proportions
Same angles
Same size
Same orientation
Different position

The object and the image are both similar and congruent

Question 18

Are all similar shapes congruent?

Answer 18

No, similar shapes can be bigger or smaller versions of each other

Question 19

Are all congruent shapes similar?

Answer 19

Yes, it’s usually said that all congruent shapes have the same proportions and angles, so congruent shapes are both similar and congruent

Question 20

The object of a transformation is usually labelled with capital letters, eg. ABC
The image is normally labelled like this A’B’C’

What is the name of the ‘ ?

Answer 20

’ is called the prime symbol

Question 21

Properties / points that don’t change during a transformation are called

Answer 21

Invariant (as in, they don’t vary)

Question 22

When you reflect a point across the x-axis, which coordinate stays the same and which changes?

Answer 22

The x coordinate remains the same, and the y coordinate becomes its opposite (the + or - sign switches)

Question 23

When you reflect a point across the y-axis, which coordinate stays the same and which changes?

Answer 23

The y coordinate remains the same and the x coordinate is transformed into its opposite (the + or - sign is switched)

Question 24

When you reflect a coordinate across the line y = x, what happens to the coordinates?

Answer 24

They swap.

x, y) becomes (y, x

Question 25

When you reflect a coordinate across the line y = -x, what happens to the coordinates?

Answer 25

They swap and also change to opposite + or - signs.

x, y) becomes (-y, -x

Question 26

Each point of a reflected image is ____ from the line of reflection as the corresponding point of the original figure

Answer 26

the same distance

Question 27

A dilation of scale factor -1 could also be described as a ____

Answer 27

point reflection

Question 28

when the points are arranged in a different way, as shown in this diagram, we say that the shape has changed its ____

Answer 28

orientation

orientation is preserved in translations, rotations and dilations, but it changes in a reflection

Question 29

A transformation in which the lengths and angles are all preserved (stay the same) is called a ____

Answer 29

rigid transformation

Question 30

Is a dilation a rigid or non-rigid transformation?

Answer 30

Non-rigid

The shape becomes larger or smaller