Rigid Motions Practice Worksheet
Rigid Motion Sequences
Coordinate Plane: Translations, Reflections & Rotations
Name:
Date:
Period:
Directions Apply each 2-step sequence to the given pre-image. Write the intermediate and final coordinates, then graph and label the final image on the grid.
1 Triangle ABC
Pre-image: Blue
Step 1: Translate: \((x, y) \to (x - 3, y - 2)\)
Step 2: Reflect across the \(y\)-axis
x y 2 4 -2 -4 2 4 -2 -4 A B C
Pre-Image
A: ( 1 , 1 )
B: ( 4 , 1 )
C: ( 1 , 4 )
After Step 1
A': (,)
B': (,)
C': (,)
Final Image
A'': (,)
B'': (,)
C'': (,)
2 Triangle DEF
Pre-image: Blue
Step 1: Reflect across the \(x\)-axis
Step 2: Translate: \((x, y) \to (x + 5, y + 1)\)
x y 2 4 -2 -4 2 4 -2 -4 D E F
Pre-Image
D: ( -4 , 1 )
E: ( -1 , 1 )
F: ( -4 , 4 )
After Step 1
D': (,)
E': (,)
F': (,)
Final Image
D'': (,)
E'': (,)
F'': (,)
3 Triangle JKL
Pre-image: Blue
Step 1: Translate: \((x, y) \to (x + 3, y + 4)\)
Step 2: Reflect across the \(y\)-axis
x y 2 4 -2 -4 2 4 -2 -4 J K L
Pre-Image
J: ( -4 , -1 )
K: ( -1 , -1 )
L: ( -2 , -4 )
After Step 1
J': (,)
K': (,)
L': (,)
Final Image
J'': (,)
K'': (,)
L'': (,)
4 Triangle PQR
Pre-image: Blue
Step 1: Rotate \(90^\circ\) CCW about \((0,0)\)
Step 2: Translate: \((x, y) \to (x, y - 3)\)
x y 2 4 -2 -4 2 4 -2 -4 P Q R
Pre-Image
P: ( 1 , 2 )
Q: ( 4 , 2 )
R: ( 1 , 4 )
After Step 1
P': (,)
Q': (,)
R': (,)
Final Image
P'': (,)
Q'': (,)
R'': (,)
Check: Rigid motions preserve congruence. Plot and label all vertices of the final image.
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