VOCABULARY
FORMULAS/THEOREMS
ROTATIONS
RIGID MOTION
WORD PROBLEMS
100
WHICH DIRECTION DOES A POSITIVE ROTATION MOVE IN
WHAT IS COUNTERCLOCKWISE
100
THE COMPOSITION OF TWO OR MORE RIGID MOTIONS
(THIS IS A THEOREM)
WHAT IS THEOREM 3-3
100
ROTATE FIGURE WXYZ 180* COUNTERCLOCKWISE
W(2,8)
X(2,2)
Y(5,2)
Z(5,3)
W'(-2,-8)
X'(-2,-2)
Y'(-5,-2)
Z'(-5,-3)
100
BOB SAYS THAT FROM UMN TO U'M'N' IT IS A RIGID MOTION. IS HE CORRECT
U (-5,5)
M (-5,8)
N (-2,7)
U' (5,5)
M' (3,4)
N' (6,2)
NO, BOB IS NOT CORRECT BECAUSE THE LENGTH AND WIDTH IS NOT PRESERVED
100
WHEN YOU ROTATE A FIGURE, DOES EVERY POINT MOVE THE SAME DISTANCE?
NO, THEY DO NOT MOVE THE SAME DISTANCE, THEY ONLY MOVE THE AMOUNT NECESSARY FOR THE GIVEN CIRCUMSTANCE, WHICH DEPENDS ON THE POSITION OF THE GIVEN POINT
200
THE POINT IN WHICH A ROTATION IS BASED AROUND
WHAT IS CENTER OF ROTATION
200
(not exactly a formula but something important to remember)
NAME THE DIFFERENT TYPES OF RIGID MOTION
WHAT IS TRANSLATION, REFLECTION, ROTATION, AND GLIDE REFLECTION
200
ROTATE FIGURE JKL 90* CLOCKWISE
J(3,1)
K(5,1)
L(4,3)
J'(1,-3)
K'(1,-5)
L'(3,-4)
200
REFLECT FIGURE ABC ACROSS THE Y-AXIS
TRANSLATE FOR THE FOLLOWING POINTS USING Ry-axis o T(0,-4)
A (1,2)
B (1,4)
C (3,3)
Ry-axis o T(0,-4)
A' (-1,2)
B' (-1,4)
C' (-3,3)
A'' (-1,-2)
B'' (-1,0)
C'' (-3,-1)
200
TRIANGLE ABC IS ROTATED 36 CLOCKWISE AND TRANSLATED (0,-4). IS THIS A RIGID MOTION?
YES
300
A TRANSFORMATION THAT ROTATES EACH POINT IN THE PREIMAGE ABOUT A GIVEN POINT
WHAT IS ROTATION
300
ANY RIGID MOTION THAT IS EITHER A TRANSLATION, REFLECTION, ROTATION, OR GLIDE REFLECTION
(THIS IS A THEOREM)
WHAT IS THEOREM 3-4
300
ROTATE FIGURE GHI 270* COUNTERCLOCKWISE
G (8, -3)
H (-4, 2)
I (8, -6)
G' (-3, -8)
H' (-2, -4)
I' (-6, -8)
300
A COMPOSITION OF TWO OR MORE RIGID MOTIONS IS CALLED...
(dont overthink it-)
WHAT IS RIGID MOTION
300
JESSICA SAYS THAT THE MOVEMENT OF TRIANGLE LMN TO TRIANGLE L'M'N' IS NOT A RIGID MOTION BECAUSE THE POSITION OF TRIANGLE OF LMN CHANGED
IS JESSICA CORRECT
NO, JESSICA IS INCORRECT BECAUSE THE POSITION OF LMN CHANGED, BUT THE LENGTH AND ANGLE MEASURES STAYED THE SAME
400
A TRANSFORMATION THAT PRESERVES LENGTH AND ANGLE MEASURE (ISOMETRY)
WHAT IS RIGID MOTION
400
WHAT IS A 90* ROTATION COUNTERCLOCKWISE TURNED INTO A CLOCKWISE ROTATION
(-y,x)
WHAT IS 270* CLOCKWISE
(-y,x)
400
ROTATE FIGURE ABCD 90* CLOCKWISE
A(5,7)
B(5,-8)
C(0,2)
D(0, -4)
A'(-7,5)
B'(8,5)
C'(-2,0)
D'(4,0)
400
SOLVE
T(0,-2) o Ry-axis
A (6,-4)
B (3,8)
C (-7,9)
TRIANGLE ABC = TRIANGLE A'B'C'
A' (-6,-6)
B' (-3,6)
C' (7,7)
400
TRIANGLE JKL IS ROTATED OVER TWO INTERSECTING LINES WITH A DEGREE OF 60
WHAT IS HALF OF THE ANGLE OF ROTATION
A. 35
B. 40
C. 30
D. 60
C. 30
500
A COMPOSITION OF A TRANSFORMATION CONSISTING OF TWO OR MORE RIGID MOTIONS
WHAT IS GLIDE REFLECTION
500
ANY ROTATION IS A COMPOSITION OF REFLECTIONS ACROSS TWO LINES THAT INTERSECT AT THE CENTER OF ROTATION
WHAT IS THEOREM 3-2
500
Ra o Rb
r(40*,p)
WHAT IS THE ROTATION OF THIS DEGREE
(Hint: /2)
WHAT IS 20*
500
SOLVE
T (0,8) o Rm
J (6,-4)
K (3,8)
L (-7,9)
SUPPOSE m IS x=-3
J' (-12,-4)
K' (-9,8)
L' (1,9)
500
JEFF ROTATES TRIANGLE ABC 90 COUNTERCLOCKWISE
A (-1,2) ----- A' (2,1)
B (4,-9) ----- B' (-9,-4)
C (3,-3) ----- C' (-3,-3)
WHAT IS JEFF'S MISTAKE?
A. HE MISCALCULATED
B. HE ROTATED THE WRONG WAY
C. NOTHING; HE IS CORRECT
B. HE ROTATED THE WRONG WAY
A' (-2,-1)
B' (-4, 9)
C' (3,-3)