Transformations Unit

Question 1

What are the 2 components of polar coordinates?

Answer 1

(r , ϴ ) - Radius and direction

Question 2

What are the different types of transformations?

Answer 2

Translations, rotations, reflections and dilations

Question 3

What is an isometry?

Answer 3

An isometry occurs when the transformed figure is congruent to the original one

Question 4

Which transformations give an isometry?

Answer 4

Translations, rotations, and reflections

Question 5

Which transformations do not give an isometry?

Answer 5

Dilations

Question 6

When a dilation occurs, what is the relationship between the two figures?

Answer 6

They are similar

Question 7

How do you define a translation?

Answer 7

T(x , y) = (x ± a , y ± b)

Question 8

How do you define a rotation?

Answer 8

R(0 , ϴ)

Question 9

How do you define a dilation?

Answer 9

D( P , k )

Question 10

If D is at (x , y) and reflected about the y axis, what are the coordinates of D’?

Answer 10

(-x , y)

Question 11

If F is at (x , y) and reflected about the x axis, what are the coordinates of F’?

Answer 11

(x , -y)

Question 12

If H is at (x, y) and rotated by R(O,90°) what are the coordinates of H’?

Answer 12

(-y , x)

Question 13

If I is at (x, y) and rotated by R(O,180°) what are the coordinates of I’?

Answer 13

(-x , -y)

Question 14

The equation of all vertical lines takes what form?

Answer 14

x = a

Question 15

The equation of all horizontal lines takes what form?

Answer 15

y = b

Question 16

If B is at (7,8) and B’ is at (7,2) what was the axis of reflection?

Answer 16

y = 5

Question 17

If C is at (-3,2) and C’ is at (11,2) what was the axis of reflection?

Answer 17

x = 4

Question 18

Given the point A at (5,8), what is the coordinate of A’ if it is translated by T(x,y) = (x-1 , y-2)

Answer 18

(4 , 6)

Question 19

Given the point A at (5,8), what is the coordinate of A’ if it is dilated by D( O, 1/2 )?

Answer 19

(5/2 , 4)

Question 20

Given the point A at (5,8), what is the coordinate of A’ if it is reflected about the x axis?

Answer 20

(5 , -8)

Question 21

Given the point A at (5,8), what is the coordinate of A’ if it is reflected about the y axis?

Answer 21

(-5 , 8)

Question 22

Given the point A at (5,8), what is the coordinate of A’ if it is rotated by 90º?

Answer 22

(-8 , 5)

Question 23

Given the point A at (5,8), what is the coordinate of A’ if it is rotated by 180º?

Answer 23

(-5 , -8)

Question 24

Given the point A at (5,8), what is the coordinate of A’ if it is reflected about the y = 2?

Answer 24

(5 , -4)

Question 25

Given the point A at (5,8), what is the coordinate of A’ if it is reflected about x = 3?

Answer 25

(1 , 8)

Question 26

Given the point A at (5,8), what is the coordinate of A’ if it is dilated by D(P , 2) if P is at (1,3)?

Answer 26

(9 , 13)

Question 27

Describe how you can tell if a figure has rotational (point) symmetry.

Answer 27

If there exists a number of degrees (less than 360º) for which you can rotate the figure around its center and result in an identical figure to the original (in every way).

Question 28

What are the 3 types of symmetries?

Answer 28

Vertical line symmetry, horizontal line symmetry, and rotational/point symmetry

Question 29

Describe how you can tell if a figure has vertical line symmetry.

Answer 29

If a vertical line drawn through the center of the figure makes the left and right sides reflections of each other

Question 30

Describe how you can tell if a figure has horizontal line symmetry.

Answer 30

If a horizontal line drawn through the center of the figure makes the top and bottom reflections of each other.