Unit 6: Transformations (Ch 9)

Question 1

transformation

Answer 1

A transformation moves or changes a figure to produce a new figure.

Question 2

preimage

Answer 2

The original figure is called the preimage.

Question 3

image

Answer 3

The new figure is called the image.

Question 4

transformation statement

Answer 4

A transformation statement describes the “mapping” of each preimage point to its image point. EX: ABC ==> A’B’C’
(Explains how the preimage points will move to the image points.)

Question 5

prime notation

Answer 5

Use prime notation to name an image. EX: ABC ==> A’B’C’

This labels the image so that it is not confused with the preimage. It is an apostrophe

Question 6

reFLection

Answer 6

FLip - a mirror image of the original figure.

Question 7

tranSLation

Answer 7

SLide - moves every point of a figure the same distance in the same direction.

Question 8

roTation

Answer 8

Turn - a figure is turned about a fixed point.

Question 9

diLationS

Answer 9

Larger or Smaller - a figure is enlarged or reduced.

Question 10

congruence transformation

Answer 10

Changes the position of the figure without changing its size or shape.

Question 11

isometry

Answer 11

Another word for “congruence statement.” Changes the position of the figure without changing its size or shape.
All transformations are isometries, EXCEPT dilations!

Question 12

reflection

Answer 12

A reflection uses a line of reflection to create a mirror image of the original image.

Question 13

REFLECTION

In reflection, what two things are the same distance from the line of reflection?

Answer 13

In reflection, each point of the preimage and its corresponding point in the image are the same distance from the line of reflection.

Question 14

REFLECTION

What information do we know if the point is on the line of reflection?

Answer 14

If the point is on the line of reflection, then the image and preimage are the same point.

Question 15

REFLECTION

What information do we know if the point does NOT lie on the line of reflection?

Answer 15

If the point does NOT lie on the line of reflection, the line of reflection is the perpendicular bisector of the segment joining the two points.

Question 16

REFLECTION COORDINATE RULES

Reflecting over the x - axis

Answer 16

(x, y) ==> (x, -y)

Change the sign of the y coordinate.

Question 17

REFLECTION COORDINATE RULES

Reflecting over the y - axis

Answer 17

(x, y) ==> (-x, y)

Change the sign of the x coordinate.

Question 18

REFLECTION COORDINATE RULES

Reflecting over the line y = x

Answer 18

(x, y) ==> (y, x)

Swap the x and y coordinates.

Question 19

REFLECTION COORDINATE RULES

Reflecting over the line y = -x

Answer 19

(x, y) ==> (-y, -x)

Swap the x and y coordinates and change the sign of both of the new x and y coordinates.

Question 20

translation

Answer 20

A translation moves every point of a figure the same distance in the same direction.

Question 21

TRANSLATION

coordinate notation for a translation

Answer 21

(x, y) ==> (x+a, y+b)
Each point (x, y) is translated horizontally "a" number of units and vertically "b" number of units.

Question 22

TRANSLATION

vector notation for a translation

Answer 22

<a>
This tells us how many units each point will slide.
“a” tells us what direction the x coordinates will move and “b” will tell us what direction the y coordinates will move.</a>

Question 23

rotation

Answer 23

A rotation turns a figure about a fixed point called the center of rotation.

Question 24

ROTATION

Which direction is a rotation understood to move?

Answer 24

Rotations are counterclockwise (CCW), unless stated to be clockwise (CW).

Question 25

ROTATION
Coordinate rules for rotations about the origin (CCW)
For a rotation of 90°

Answer 25

(x, y) ==> (-y, x)

Swap the x and y coordinates and chance the sign of the new x coordinate.

Question 26

ROTATION
Coordinate rules for rotations about the origin (CCW)
For a rotation of 180°

Answer 26

(x, y) ==> (-x, -y)

Change the signs of the x and y coordinates.

Question 27

ROTATION
Coordinate rules for rotations about the origin (CCW)
For a rotation of 270°

Answer 27

(x, y) ==> (y, -x)

Swap the x and y coordinates and change the sign of the new y coordinate.

Question 28

Solid of revolution

Answer 28

A three-dimensional figure obtained by rotation a place figure (two-dimensional figure) or curve about a line. Three-dimensional figures can be generated by rotation two-dimensional figures around an imaginary line called a rotation axis.
EX: rotating a two-dimensional triangle about a rotation axis becomes a cone.
EX: rotating a two-dimensional rectangle about a rotation axis becomes a cylinder.

Question 29

compositions of transformations

Answer 29

When two or more transformations are combined to form a single transformation.

Question 30

line of symmetry

Answer 30

A figure has a line symmetry if the figure can be mapped onto itself by a *** in a line.
The line of reflection in line symmetry.