Geometric Transformations Flashcards
Translations can be described in what three ways?
In words
As an algebraic rule
As a vector
Rotations are described by what three things?
Centre of rotation
Direction of rotation (clockwise or counter-clockwise / anti-clockwise)
Angle of rotation
Reflections are described by the ____
Line of reflection
Dilations / enlargements on a coordinate plane are described by the
Centre point
Scale factor
Dilations can make a shape bigger or smaller. What are the mathematical terms for this?
Expansion / enlargement and contraction / reduction
A dilation is an expansion / enlargement if its scale factor is
Greater than 1
A dilation is a contraction if its scale factor is
Between 0 and 1
A dilation of scale factor 1 would ____
not change the object.
A transformation transforms a shape from a(n) ____ to an ____
from an object / pre-image to an image
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’)
perpendicular bisector
Will a fractional scale factor always make the image of a dilation smaller than the object?
No, the fraction could be greater than 1, which would be an expansion / enlargement of the object.
What stays the same and what changes when a shape is dilated?
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)
When a plane figure (2D shape) is dilated by scale factor 2, what happens to the side lengths and what happens to the area?
The side lengths double (x2)
The area quadruples (x2 squared, or x4)
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?
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”
What stays the same and what changes when a shape is rotated?
Same proportions
Same angles
Same size
Same orientation
The object and the image are congruent (and also similar)
What stays the same and what changes in a reflection?
Same proportions
Same angles
Same size
Different orientation
The object and the image are congruent and similar.
What stays the same and what changes in a translation?
Same proportions Same angles Same size Same orientation Different position
The object and the image are both similar and congruent
Are all similar shapes congruent?
No, similar shapes can be bigger or smaller versions of each other
Are all congruent shapes similar?
Yes, it’s usually said that all congruent shapes have the same proportions and angles, so congruent shapes are both similar and congruent
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 ‘ ?
’ is called the prime symbol
Properties / points that don’t change during a transformation are called
Invariant (as in, they don’t vary)
When you reflect a point across the x-axis, which coordinate stays the same and which changes?
The x coordinate remains the same, and the y coordinate becomes its opposite (the + or - sign switches)
When you reflect a point across the y-axis, which coordinate stays the same and which changes?
The y coordinate remains the same and the x coordinate is transformed into its opposite (the + or - sign is switched)
When you reflect a coordinate across the line y = x, what happens to the coordinates?
They swap.
x, y) becomes (y, x
When you reflect a coordinate across the line y = -x, what happens to the coordinates?
They swap and also change to opposite + or - signs.
x, y) becomes (-y, -x
Each point of a reflected image is ____ from the line of reflection as the corresponding point of the original figure
the same distance
A dilation of scale factor -1 could also be described as a ____
point reflection
when the points are arranged in a different way, as shown in this diagram, we say that the shape has changed its ____
orientation
orientation is preserved in translations, rotations and dilations, but it changes in a reflection
A transformation in which the lengths and angles are all preserved (stay the same) is called a ____
rigid transformation
Is a dilation a rigid or non-rigid transformation?
Non-rigid
The shape becomes larger or smaller
