Transformations

Question 1

Line symmetry

Answer 1

Congruent if folded horizontally vertically or diagonally along an imaginary line

Question 2

Point symmetry

Answer 2

If identical when rotated 180 degrees upside down

Question 3

r x-axis

Answer 3

Reflect over x axis, negate y

Question 4

r y-axis

Answer 4

Reflect over y axis negate x

Question 5

r y=x

Answer 5

Diagonal up, flip (y,x)

Question 6

r y=-x

Answer 6

Diagonal down, flip/negate both (-y,-x)

Question 7

What is not preserved in a line reflection?

Answer 7

Orientation

Question 8

R 360

Answer 8

Original (a,b)

Question 9

R 90

Answer 9

(-b,a)

Question 10

R 180

Answer 10

(-a,-b) same as point reflection through origin

Question 11

R 270

Answer 11

(b,-a)

Question 12

R -270

Answer 12

(-b,a)

Question 13

R -180

Answer 13

(-a,-b)

Question 14

R -90

Answer 14

(b,-a) negatives go clockwise

Question 15

What is preserved under rotation?

Answer 15

Distance, orientation, midpoint, collinearity, angle measure

Question 16

Rotational symmetry

Answer 16

Figure is the same under a rotation, for regular shapes divide 360/#sides for the order of rotational symmetry

Question 17

R o

Answer 17

Point reflection through the origin, (-x,-y)

Question 18

How do you reflect though points other than the origin?

Answer 18

Find the rise and run from the point to the point you are reflecting over and continue the line with that slope so the point you are reflecting over is the midpoint

Question 19

What is a glide reflection?

Answer 19

Composition of a translation and a line reflection, orientation is not preserved

Question 20

A composition of 2…

Answer 20

Translations is a translationRotations is a rotation

Question 21

(Don’t have to memorize but good to know) A composition of 2 line reflections through…

Answer 21

Parallel lines is a translation Perpendicular lines is a point reflectionIntersecting lines is a rotation

Question 22

What is Isometry/rigid motion, and an example of not isometric?

Answer 22

Transformations that preserve distance, dilations are the only ones not isometric

Question 23

Direct Isometry

Answer 23

Preserves orientation:TranslationsRotationsPoint reflections

Question 24

Opposite Isometry

Answer 24

Does not preserve orientation:Line reflectionsGlide reflections

Question 25

How do you know if it preserves orientation?

Answer 25

Write out the order of point going clockwise for both figures and see if it’s in the same order e.g. ABCABCABC vs BCABCABCA has preserved orientation