Transformations

Question 1

What does it mean to preserve distance?

Answer 1

Lengths of segments are the same

Question 2

What does it mean to preserve angle measure?

Answer 2

Angles stay the same

Question 3

What does it mean to maintain parallelism?

Answer 3

Things that were parallel are still parallel

Question 4

What does it mean to maintain collinearity?

Answer 4

Points on a line stay on the line

Question 5

What is a rigid motion?

Answer 5

A transformation preserving distance, angle measure, parallelism, & collinearity

Question 6

What does a rigid mroion to ensure?

Answer 6

Resulting figure is same size & shape (congruent image & pre image)

Question 7

Which transformation is NOT a rigid motion?

Answer 7

Dialation- not same size

Question 8

What is a stretch?

Answer 8

One dimension’s scale factor is different than the other dimension’s scale factor

Question 9

What is a dialation?

Answer 9

The scale factor is the same for both dimensions, producing a PORPORTIONAL but not IDENTICAL shape

Question 10

What are the properties of a translation (slide)

Answer 10

1. Distances are the same- AA’ is congruent to BB’
2. Orientation (way something is angled) is the same
3. Each translated segment is parallel to its image ex. AC is parallel to A’C’

Question 11

Translation mapping

Answer 11

(x,y) —> (x-7, y-3)

Question 12

Translation description

Answer 12

7 units left and 3 units down

Question 13

Translation notation

Answer 13

T(x,y), T(-7,-3)

Question 14

Translation vector

Answer 14

___
V = (-7,-3)

Question 15

How to find vector that defines translation &magnitude

Answer 15

1. Count spaces between both images
   Ex. 3to the second power + 2to the second power= V*to the second power
   Square root for answer

Question 16

What do you write when finding the rule describing the given translation?

Answer 16

T(x,y)

Question 17

What is a reflection?

Answer 17

A rigid motion where each point of the pre image has an image that is the same distance from the LoR as the original point (on the opposite side of the line)

Question 18

What is the line of reflection?

Answer 18

The perpendicular bisector of the segment

Question 19

Reflection properties #1- if point P is not on line m, what is line m?

Answer 19

The perpendicular bisector of PP’

Question 20

Reflection properties #2- what is point p if it is on line m?

Answer 20

Congruent to P’ P=P’

Question 21

What is reversed about the figure in a reflection?

Answer 21

Orientation

Question 22

Line reflection rule #1- reflected over x axis

Answer 22

(x,y) to (x,-y)

Question 23

Line reflection rules #2- reflected over the y axis

Answer 23

(x,y) to (-x,y)

Question 24

Line reflection rules #3- when y=x and y=-x

Answer 24

FLIP- (x,y) to (y,x) / (x,y) to (-y,-x)

Question 25

What is function notation

Answer 25

R (P) = P’
m

Question 26

What is line of symmetry/reflectional symmetry?

Answer 26

A line can be drawn through the figure so both sides of the figure are mirror images of the other (there can be more than one LoS or no LoS)

Question 27

What is point symmetry?

Answer 27

The figure is the same image when rotated 180 degrees, or turned upside down (looks the same!)

Question 28

What us always true about reflections?

Answer 28

The segments of both the image and pre image are congruent to each other

Question 29

Point F is on one side of line g and is exactly 4 cm away from line g. Point H is on the opposite side of line g and is also exactly 4cm away from line g- is it safe to say Point H is the reflection of Point F?

Answer 29

No- there is no proof line g is the perpendicular bisector

Question 30

What changes in the properties of rotations?

Answer 30

The distances are different- points on the plane move different distances, depending on distance from center of rotation. The image and pre-image segments are not parallel to each other because of incongruous distances

Question 31

What stays the same in rotation properties?

Answer 31

Orientation & Special points- center of rotation is invariant (constant)

Question 32

Rotation of 90 degrees

Answer 32

(x,y) to (-y,x)

Question 33

Rotation of 180 degrees

Answer 33

(x,y) to (-x,-y) flip!!

Question 34

Rotation of 270 degrees

Answer 34

(x,y) to (y,-x)

Question 35

After a figure is rotated, A = A’. What does this mean?

Answer 35

The center of rotation is A (why?)

Question 36

How do rotations differ from reflections & translations?

Answer 36

Not translation- each point moves different distances
Not reflection- same orientation

Question 37

Why isn’t dilation a rigid motion?

Answer 37

It does not preserve distance

Question 38

What does every dialation have?

Answer 38

A center (generally origin( and scale factor n

Question 39

What is the dialation called if the scale factor n>1?

Answer 39

Enlargement

Question 40

What is the dilation called if 0

Answer 40

Reduction

Question 41

What happens if the scale factor in a dialation is 1?

Answer 41

Nothing

Question 42

Dialation notation

Answer 42

D (x, y) = (kx, ky)
O,k O= center of dialation, k= scale factor

Question 43

Which properties ARE preserved in dilations?

Answer 43

Angle measures (angles are the same), Parallelism (dilations create parallel lines between all pre image and image corresponding segments), and Collinearity (points on the line remain on that line)