Stations for Transformation Exploration
Station Check list:
______1) Translations
______2) Reflections
______3) Rotations
______4) Reflections over odd/even # of parallel lines
______5) Reflections over parallel lines as translations
______6) Rotations as reflections over intersecting lines
Station #1: Translations
1) Look at your coordinates for the TV stand before and after the translation.
Decide what type of translation this would be… horizontal, vertical or both.
_____________________
2) Which coordinate changed in this translation? _______
By how many units (feet)?_____
3) The Harrison’s need more floor space for Charades Game Night. Please
translate the coffee table so it is to the far right of the room against the
window and then 2.5 feet up so it is flush with the edge of the window.
Write the new coordinates for the 4 corners:
Corner 1
coordinates
Corner 2
coordinates
Corner 3
coordinates
Corner 4
coordinates
4) Would you describe a translation as a flip, turn or slide?__________
5) Now, try to explain what a translation rule might be for moving a coordinate
( x, y) 3 left and 4 down.
What would the rule be for any (x,y) coordinate?
Station #2: Reflections
1) Look at your coordinates for the sofa before and after the reflection.
State the pattern you notice.
2) Hypothesize what you think would happen to the coordinates ( x, y) if they
were reflected over the y-axis.
3) How many units away from the x-axis was the sofa in the before
plan?_________
4) How many units away from the x-axis is the sofa after the reflection
plan?_________
5) Using your answers in #3 and #4, what pattern do you notice about reflecting
an object over its line of reflection?
6) Would you describe a reflection as a flip, turn or slide?__________
What would the rule be for any (x,y) coordinate?
Station #3: Rotations
1) Look at your coordinates for either bookcase before and after the rotation of
90 degrees clockwise. State the pattern you notice.
2) Use your before paper, and now turn the paper upside down (180 degrees),
what are the new corner 1 bookcase coordinates?_______
Is this the same pattern as rotating it 90 degrees clockwise? ______
3) Use your before paper, and now turn the paper 270 degrees counter
clockwise what are the new corner 1 bookcase coordinates?_______
Is this the same pattern as rotating it 90 degrees clockwise? ______
4) Would you describe a rotation as a flip, turn or slide?__________
5) Match each: Find the matching rotation that would yield the same results.
_____A. rotation 90o clockwise
1. rotation 90ocounter clockwise
_____B. rotation 180 o clockwise
2. rotation 180ocounter clockwise
_____C. rotation 270 o clockwise
3. rotation 270ocounter clockwise
What would the rule be for any (x,y) coordinate rotation of 90o?
Station #4: Reflections over odd/even # of parallel lines
Graphing Activity
1) Graph the vertices of triangle PEA, P(-3, 9) E ( -3, 7) and A( -1, 7).
2) Now reflect triangle PEA over the line y = 6. Label the corresponding
vertices P’ E’ and A’.
3) Now reflect triangle P’E’A’ over the parallel line y = 1. Label the
corresponding vertices P’’ E’’ and A’’.
4) Now reflect triangle P’’E’’A’’ over the parallel line y = -5. . Label the
corresponding vertices P’’’ E’’’ and A’’’.
5) Now consider the orientation for each.
Triangle
Orientation CW or CCW
PEA
P’E’A’
P’’E’’A’’
P’’’E’’’A’’’
6) Do you notice a pattern between orientation and the number of lines of
reflection? Explain.
Station #5: Reflections over parallel lines as translations
Graphing Activity
Reflections
1) Graph the vertices of parallelogram TWIX where T(6,5) W (8, 5) I (7,3) and
X (5, 3).
2) Now, reflect this over the line x=3 (rx=3TWIX), label the resulting image
T’W’I’X’.
3) Now, reflect parallelogram T’W’I’X’ over the line x= -3(rx=-3T’W’I’X’), label
the resulting image T’’W’’I’’’X’’.
Translations
1) Graph the vertices of parallelogram TWIX
where T (6,5) W (8, 5) I (7,3) and X (5, 3).
2) Now translate parallelogram TWIX
12 units left. (T12,0 TWIX)
Compare these 2 rigid motions:
Station #6: Rotations as reflections over intersecting lines
Graphing Activity #1:
1) Graph the pre-image “L” by connecting these points in sequence:
(6,3) to (4,3) to (4,7).
2) Now reflect this image over the x-axis then over the y-axis.
NOTE: The x and y axis are intersecting lines.
3) Now could you map the pre-image L to the final image after 2 reflections
using a rotation? If so, explain.
Graphing Activity #2:
1) Graph the intersecting lines, y= x and y=-x.
2) Graph the pre-image “L” by connecting these points
in sequence: (1,2) to (-1,2) to (-1,6).
3) Reflect this pre-image over the line y= x
then over the y=-x.
4) Now could you map the pre-image L to
the final image after 2 reflections using a
rotation? If so, explain
Station # 1
Station #2
Station #3