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Puzzling Transformations
Bundle Art Activities with
Translations, Reflections,
Rotations & Dilations
Common Core ~ 8.G.A.3
Rockin’ Middle School Math
Puzzling
Transformations
Objective: 8.G.A.3
Describe the effect of dilations, translations, rotations and
reflections on two-dimensional figures using coordinates.
Puzzle # 1: 2-step Translations
Puzzle # 2: Reflections over the x-axis and the y-axis.
Puzzle # 3: Reflections and Translations (1 and 2-steps)
Puzzle # 4: Rotations Clockwise and Counter-Clockwise about
the Origin, including 90°, 180°, and 270°
Puzzle # 5: Translations, Reflections, and Rotations
(1 and 2-steps)
Puzzle # 6: Dilations about the Origin
Puzzle # 7: All 4 types of transformations (1-step only)
Puzzle # 8: All 4 types of transformations (2-steps)
Transformation Puzzles Objective:
8.G.A.3 – Describe the effect of dilations, translations, rotations and reflections on two-
dimensional figures using coordinates.
Materials:
One copy of student worksheet per student
One copy of 4 quadrant coordinate plane
Colored pencils, markers or crayons
One ruler per student
Procedure:
Students should use the rules for the different transformations described on each
worksheet and then plot the resulting points on the coordinate plane. I have
attached a cheat sheet giving the rules for each type of transformation if you feel
that the students could benefit from it.
Students will then use a ruler to connect the points to make each figure.
Students can color their picture when all of the pieces are complete. They can add
other drawings/objects to the picture to decorate it nicely.
None of the transformations will overlap, so if a student has two images overlapping,
he/she made a mistake.
Alternate Ideas:
Students could plot and connect the Pre-Image points on another sheet of graph
paper. They could then manually complete the transformations.
Plot and connect the Pre-Image points on another sheet of graph paper, cut them out,
and use them to manually transform the figures on another sheet of graph paper.
The Pre-Image points could be plotted and connected on a graph dry erase board.
The students could then transform them on the board and copy them on to graph
paper.
Name:_________________________ Date:__________________________
Puzzle # 1: Perform each transformation using the
given pre-image points. Plot the points of the new
image on the provided coordinate plane. Connect
the points in each problem to make a polygon. When
done, you may color your design.
1. Translate Pre Image coordinates left
6 units and down 15 units.
A (8, 17) B (8, 11) C (2, 11)
Post Image Coordinates:
A’ _______ B’ _______ C’ _______
2. Translate Pre Image coordinates right 8
units and up 7 units.
A (-6,-11) B (-12, -11) C (-12, -17)
Post Image Coordinates:
A’ _______ B’ _______ C’ _______
3. Translate Pre Image coordinates using
the rule (x + 18) and (y – 12).
A (-6, 15) B (-8, 7) C (-11, 12)
Post Image Coordinates:
A’ _______ B’ _______ C’ _______
4. Translate Pre Image coordinates using
the rule (x - 13) and (y + 21).
A (3, -5) B (10, -8) C (12, -13) D (5, -10)
Post Image Coordinates:
A’ _____B’_______C’_______ D’_______
5. Translate Pre Image coordinates left
9 units and down 1 unit.
A (11, 9) B (11, 3) C (5, 3) D (5, 9)
Post Image Coordinates:
A’ ______B’______C’______D’_______
6. Translate Pre Image coordinates right
14 units and up 13 units.
A (-12,3) B (-6, -3) C (-12, -9)
Post Image Coordinates:
A’ _______ B’ _______ C’ _______
7. Translate Pre Image coordinates using
the rule (x + 7) and (y + 2).
A (-5, 1) B (3, -7) C (-5, -15)
Post Image Coordinates:
A’ _______ B’ _______ C’ _______
8. Translate Pre Image coordinates using
the rule (x + 10) and (y – 19).
A (0, 14) B (0, 3) C (-11, 3)
Post Image Coordinates:
A’ _______ B’ _______ C’ _______
Translations: Rabbit
1. Translate Pre Image coordinates
left 6 units and down 15 units.
A (8, 17) B (8, 11) C (2, 11)
Post Image Coordinates:
A’ (2, 2) B’ (2, -4) C’ (-4, -4)
2. Translate Pre Image coordinates
right 8 units and up 7 units.
A (-6,-11) B (-12, -11) C (-12, -17)
Post Image Coordinates:
A’ (2, -4) B’ (-4, -4) C’ (-4, -10)
3. Translate Pre Image coordinates
using the rule (x + 18) and (y – 12).
A (-6, 15) B (-8, 7) C (-11, 12)
Post Image Coordinates:
A’ (12, 3) B’ (10, -5) C’ (7, 0)
4. Translate Pre Image coordinates
using the rule (x - 13) and (y + 21).
A (3, -5) B (10, -8) C (12, -13) D (5, -10)
Post Image Coordinates: A’ (-10, 16) B’ (-3, 13) C’ (-1, 8) D’ (-8, 11)
5. Translate Pre Image coordinates
left 9 units and down 1 unit.
A (11, 9) B (11, 3) C (5, 3) D (5, 9)
Post Image Coordinates:
A’ (2, 8) B’ (2, 2) C’ (-4, 2) D’ (-4, 8)
6. Translate Pre Image coordinates
right 14 units and up 13 units.
A (-12,3) B (-6, -3) C (-12, -9)
Post Image Coordinates:
A’ (2, 16) B’ (8, 10) C’ (2, 4)
7. Translate Pre Image coordinates
using the rule (x + 7) and (y + 2).
A (-5, 1) B (3, -7) C (-5, -15)
Post Image Coordinates:
A’ (2, 3) B’ (10, -5) C’ (2, -13)
8. Translate Pre Image coordinates
using the rule (x + 10) and (y – 19).
A (0, 14) B (0, 3) C (-11, 3)
Post Image Coordinates:
A’ (10, -5) B’ (10, -16) C’ (-1, -16)
Puzzle # 1: Key
Name:_________________________ Date:__________________________
Puzzle # 2: Perform each transformation using
the given pre-image points. Plot the points of the
new image on the provided coordinate plane.
Connect the points in each problem to make a
polygon. When done, you may color your design.
1. Reflect Pre Image coordinates over
the y axis.
A (6, 16) B (8, 12) C (12, 14)
Post Image Coordinates:
A’________ B’________ C’________
2. Reflect Pre Image coordinates over
the x axis.
A (-1, -17) B (0, -12) C (-5, -11) D (-6, -16)
Post Image Coordinates:
A’______ B’______ C’______ D’_______
3. Reflect Pre Image coordinates over
the x axis.
A (-4, -11) B (6, -11) C (-4, -1)
Post Image Coordinates:
A’________ B’________ C’________
4. Reflect Pre Image coordinates over
the y axis.
A (0, 5) B (0, -5) C (10, -5)
Post Image Coordinates:
A’________ B’________ C’________
5. Reflect Pre Image coordinates over
the x and then the y axis.
A (7, 5) B (12, 10) C (12, 5)
Post Image Coordinates:
A’________ B’________ C’________
6. Reflect Pre Image coordinates over
the x and then the y axis.
A (0, -3) B (-6, 3) C (0, 9)
Post Image Coordinates:
A’________ B’________ C’________
7. Reflect Pre Image coordinates over
the y axis.
A (-9, 9) B (-5, 5) C (0, 5) D (-4, 9)
Post Image Coordinates:
A’______ B’______ C’______ D’______
8. Reflect Pre Image coordinates over
the x axis.
A (1, 8) B (1, 14) C (-2, 11)
Post Image Coordinates:
A’________ B’________ C’________
Reflections: Dancer
1. Reflect Pre Image coordinates over
the y axis.
A (6, 16) B (8, 12) C (12, 14)
Post Image Coordinates:
A’ (-6, 16) B’ (-8, 12) C’ (-12, 14)
2. Reflect Pre Image coordinates over
the x axis.
A (-1, -17) B (0, -12) C (-5, -11) D (-6, -16)
Post Image Coordinates: A’ (-1, 17) B’ (0, 12) C’ (-5, 11) D’ (-6, 16)
3. Reflect Pre Image coordinates over
the x axis.
A (-4, -11) B (6, -11) C (-4, -1)
Post Image Coordinates:
A’ (-4, 11) B’ (6, 11) C’ (-4, 1)
4. Reflect Pre Image coordinates over
the y axis.
A (0, 5) B (0, -5) C (10, -5)
Post Image Coordinates:
A’ (0, 5) B’ (0, -5) C’ (-10, -5)
5. Reflect Pre Image coordinates over
the x and then the y axis.
A (7, 5) B (12, 10) C (12, 5)
Post Image Coordinates:
A’ (-7, -5) B’ (-12, -10) C’ (-12, -5)
6. Reflect Pre Image coordinates over
the x and then the y axis.
A (0, -3) B (-6, 3) C (0, 9)
Post Image Coordinates:
A’ (0, 3) B’ (6, -3) C’ (0, -9)
7. Reflect Pre Image coordinates over
the y axis.
A (-9, 9) B (-5, 5) C (0, 5) D (-4, 9)
Post Image Coordinates: A’ (9, 9) B’ (5, 5) C’ (0, 5) D’ (4, 9)
8. Reflect Pre Image coordinates over
the x axis.
A (1, 8) B (1, 14) C (-2, 11)
Post Image Coordinates:
A’ (1, -8) B’ (1, -14) C’ (-2, -11)
Puzzle # 2: Key
Name:_________________________ Date:__________________________
Puzzle # 3: Perform each transformation using
the given pre-image points. Plot the points of the
new image on the provided coordinate plane.
Connect the points in each problem to make a
polygon. When done, you may color your design.
1. Reflect Pre Image coordinates over
the y axis.
A (2, 15) B (6, 11) C (10, 15)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
2. Reflect Pre Image coordinates over the
x axis, and then translate 2 units left.
A (0, -7) B (3, -4) C (0, -1) D (-3, -4)
Post Image Coordinates:
A’______B’______ C’_______ D’_______
3. Translate Pre Image coordinates using
the rule (x - 11), then reflect over the
x axis.
A (8, 0) B (-1, 9) C (-1, 0)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
4. Reflect Pre Image coordinates over the
y axis, and then translate 15 units up.
A (-11, -1) B (-2, -10) C (-2, -1)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
5. Translate Pre Image coordinates left 9
units, and then reflect over the y axis.
A (1, 4) B (1, -2) C (7, -2)
Post Image Coordinates:
A’ _______ B’ ________ C’ ________
6. Translate Pre Image coordinates right
3 units and up 10 units.
A (-1,-5) B (-1, -15) C (-6, -10)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
7. Translate Pre Image coordinates using
the rule (y - 2), then reflect over the y
axis.
A (-2, 0) B (-8, -6) C (-2, -6)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
8. Reflect Pre Image coordinates over the
x, and then reflect over the y axis.
A (2, -15) B (2, -7) C (5, -4) D (5, -12)
Post Image Coordinates:
A’______B’______ C’_______ D’_______
Translations and Reflections: Bird
1. Reflect Pre Image coordinates over
the y axis.
A (2, 15) B (6, 11) C (10, 15)
Post Image Coordinates:
A’ (-2, 15) B’ (-6, 11) C’ (-10, 15)
2. Reflect Pre Image coordinates over
the x axis, and then translate 2
units left. A (0, -7) B (3, -4) C (0, -1) D (-3, -4)
Post Image Coordinates: A’ (-2, 7) B’ (1, 4) C’ (-2, 1) D’ (-5, 4)
3. Translate Pre Image coordinates
using the rule (x - 11), then reflect
over the x axis.
A (8, 0) B (-1, 9) C (-1, 0)
Post Image Coordinates:
A’ (-3, 0) B’ (-12, -9) C’ (-12, 0)
4. Reflect Pre Image coordinates over
the y axis, and then translate 15
units up.
A (-11, -1) B (-2, -10) C (-2, -1)
Post Image Coordinates:
A’ (11, 14) B’ (2, 5) C’ (2, 14)
5. Translate Pre Image coordinates
left 9 units, and then reflect over
the y axis.
A (1, 4) B (1, -2) C (7, -2)
Post Image Coordinates:
A’ (8, 4) B’ (8, -2) C’ (2, -2)
6. Translate Pre Image coordinates
right 3 units and up 10 units.
A (-1,-5) B (-1, -15) C (-6, -10)
Post Image Coordinates:
A’ (2, 5) B’ (2, -5) C’ (-3, 0)
7. Translate Pre Image coordinates
using the rule (y - 2), then reflect
over the y axis.
A (-2, 0) B (-8, -6) C (-2, -6)
Post Image Coordinates:
A’ (2, -2) B’ (8, -8) C’ (2, -8)
8. Reflect Pre Image coordinates over
the x, and then reflect over the y
axis. A (2, -15) B (2, -7) C (5, -4) D (5, -12)
Post Image Coordinates: A’ (-2, 15) B’ (-2, 7) C’ (-5, 4) D’ (-5, 12)
Puzzle # 3:
Key
Name:_________________________ Date:__________________________
Puzzle # 4: Perform each transformation using
the given pre-image points. Plot the points of the
new image on the provided coordinate plane.
Connect the points in each problem to make a
polygon. When done, you may color your design.
1. Rotate 90° Clockwise about the origin.
A (-4, 7) B (3, 0) C (-4, -7)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
2. Rotate 90° Counterclockwise about the
origin. A (-7, 0) B (-15, -8) C (-15, 8)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
3. Rotate 90° Clockwise about the origin.
A (3, 0) B (7, 0) C (3, -5) D (-2, -5)
Post Image Coordinates:
A’______B’______ C’_______ D’______
4. Rotate 180° Counterclockwise about the
origin.
A (1, -17) B (-2, -12) C (0, -9) D (3, -14)
Post Image Coordinates:
A’______B’______ C’_______ D’_______
5. Rotate 270° Clockwise about the
origin.
A (-3, -5) B (-12, -5) C (-7, 0)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
6. Rotate 90° Counterclockwise about the
origin.
A (-7, 0) B (-12, 5) C (-3, 5)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
7. Rotate 90° Counterclockwise about the
origin.
A (9, -3) B (4, -3) C (4, 3) D (9, 3)
Post Image Coordinates:
A’______B’______ C’_______ D’______
8. Rotate 180° Clockwise about the origin.
A (-5, -2) B (-5, 3) C (0, 7) D (0, 3)
Post Image Coordinates:
A’______B’______ C’_______ D’_______
Rotations: Candle
1. Rotate 90° Clockwise about the origin.
A (-4, 7) B (3, 0) C (-4, -7)
Post Image Coordinates:
A’ (7,4) B’ (0, -3) C’ (-7, 4)
2. Rotate 90° Counterclockwise about the
origin. A (-7, 0) B (-15, -8) C (-15, 8)
Post Image Coordinates:
A’ (0, -7) B’ (8, -15) C’ (-8, -15)
3. Rotate 90° Clockwise about the origin.
A (3, 0) B (7, 0) C (3, -5) D (-2, -5)
Post Image Coordinates:
A’ (0, -3) B’ (0, -7) C’ (-5, -3) D’ (-5, 2)
4. Rotate 180° Counterclockwise about the
origin.
A (1, -17) B (-2, -12) C (0, -9) D (3, -14)
Post Image Coordinates:
A’ (-1, 17) B’ (2, 12) C’ (0, 9) D’ (-3, 14)
5. Rotate 270° Clockwise about the
origin.
A (-3, -5) B (-12, -5) C (-7, 0)
Post Image Coordinates:
A’ (5, -3) B’ (5, -12) C’ (0, -7)
6. Rotate 90° Counterclockwise about the
origin.
A (-7, 0) B (-12, 5) C (-3, 5)
Post Image Coordinates:
A’ (0, -7) B’ (-5, -12) C’ (-5, -3)
7. Rotate 90° Counterclockwise about the
origin.
A (9, -3) B (4, -3) C (4, 3) D (9, 3)
Post Image Coordinates:
A’ (3, 9) B’ (3, 4) C’ (-3, 4) D’ (-3, 9)
8. Rotate 180° Clockwise about the origin.
A (-5, -2) B (-5, 3) C (0, 7) D (0, 3)
Post Image Coordinates:
A’ (5, 2) B’ (5, -3) C’ (0, -7) D’ (0, -3)
Puzzle # 4: Key
Name:_________________________ Date:__________________________
Puzzle # 5: Perform each transformation using
the given pre-image points. Plot the points of the
new image on the provided coordinate plane.
Connect the points in each problem to make a
polygon. When done, you may color your design.
1. Translate 5 units down and then
reflect across the x-axis.
A (-2, 12) B (9, 22) C (-2, 22)
Post Image Coordinates:
A’ _______ B’ _______ C’ _______
2. Reflect across the y-axis.
A (2, 7) B (5, 0) C (10, -2) D (7, 5)
Post Image Coordinates:
A’_____B’______ C’______ D’______
3. Translate Pre Image coordinates
right 9 units and up 2 units.
A (-8, 14) B (-10, 10) C (-13, 15)
Post Image Coordinates:
A’ _______ B’ ________ C’ _______
4. Rotate 270° clockwise about the
origin.
A (7, 2) B (0, -6) C (-7, 2)
Post Image Coordinates:
A’ _______ B’ ________ C’ _______
5. Reflect over the x-axis, and then
rotate 180° counter clockwise about
the origin.
A (2, 9) B (9, 5) C (7, 10)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
6. Rotate 90° clockwise about the
origin, and then reflect across the y-
axis. A (-12, 1) B (-11, -4) C (-6, -3) D (-7, 2)
Post Image Coordinates:
A’______B’______ C’_______ D’______
7. Reflect across the y-axis, and then
translate using the rule y + 8.
A (7, 9) B (2, 2) C (8, 3)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
8. Translate Pre Image left 4 units,
and then reflect across the x-axis.
A (10, 0) B (10, 14) C (2, 7)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
Translations, Reflections, Rotations: Indian
1. Translate 5 units down and then
reflect across the x-axis.
A (-2, 12) B (9, 22) C (-2, 22)
Post Image Coordinates:
A’ (-2,-7) B’ (9, -17) C’ (-2, -17)
2. Reflect across the y-axis.
A (2, 7) B (5, 0) C (10, -2) D (7, 5)
Post Image Coordinates: A’ (-2, 7) B’ (-5, 0) C’ (-10, -2) D’ (-7, 5)
3. Translate Pre Image coordinates
right 9 units and up 2 units.
A (-8, 14) B (-10, 10) C (-13, 15)
Post Image Coordinates:
A’ (1, 16) B’ (-1, 12) C’ (-4, 17)
4. Rotate 270° clockwise about the
origin.
A (7, 2) B (0, -6) C (-7, 2)
Post Image Coordinates:
A’ (-2, 7) B’ (6, 0) C’ (-2, -7)
5. Reflect over the x-axis, and then
rotate 180° counter clockwise about
the origin.
A (2, 9) B (9, 5) C (7, 10)
Post Image Coordinates:
A’ (-2, 9) B’ (-9, 5) C’ (-7, 10)
6. Rotate 90° clockwise about the
origin, and then reflect across the y-
axis. A (-12, 1) B (-11, -4) C (-6, -3) D (-7, 2)
Post Image Coordinates:
A’ (-1, 12) B’ (4, 11) C’ (3, 6) D’ (-2, 7)
7. Reflect across the y-axis, and then
translate using the rule y + 8.
A (7, 9) B (2, 2) C (8, 3)
Post Image Coordinates:
A’ (-7, 17) B’ (-2, 10) C’ (-8, 11)
8. Translate Pre Image left 4 units,
and then reflect across the x-axis.
A (10, 0) B (10, 14) C (2, 7)
Post Image Coordinates:
A’ (6, 0) B’ (6, -14) C’ (-2, -7)
Puzzle # 5: Key
Name:_________________________ Date:__________________________
Puzzle # 6: Perform each transformation using
the given pre-image points. Plot the points of the
new image on the provided coordinate plane.
Connect the points in each problem to make a
polygon. When done, you may color your design.
1. Dilate about the origin using a scale
factor of 2.
A (5.5, 4.5) B (6, 2) C (3.5, 1.5) D (3, 4)
Post Image Coordinates:
A’______B’______ C’_______ D’______
2. Dilate about the origin using a scale
factor of 𝟏 𝟏𝟑 .
A (11
2 , 12) B (-3, 6) C (-9, 9)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
3. Dilate about the origin using a scale
factor of 𝟏
𝟑 .
A (-12, 24) B (-30, 0) C (-36, 36)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
4. Dilate about the origin using a scale
factor of 𝟏
𝟐.
A (22, 4) B (8, -4) C (0, 10)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
5. Dilate about the origin using a scale
factor of 2.
A (3, -.5) B (3, -2.5) C (0, -4) D (0, -2)
Post Image Coordinates:
A’______B’______ C’_______ D’______
6. Dilate about the origin using a scale
factor of 4.
A (1, -1.5) B (2, -2.5) C (1, -3.5)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
7. Dilate about the origin using a scale
factor of 1.
A (0, -8) B (0, -14) C (-5, -14)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
8. Dilate about the origin using a scale
factor of .5
A (-8, 16) B (0, 10)
Post Image Coordinates:
A’ ________ B’ ________
Dilations: Walking in the Rain w/ Umbrella
1. Dilate about the origin using a scale
factor of 2.
A (5.5, 4.5) B (6, 2) C (3.5, 1.5) D (3, 4)
Post Image Coordinates:
A’ (11, 9) B’ (12, 4) C’ (7,3) D’ (6, 8)
2. Dilate about the origin using a scale
factor of 11
3 .
A (11
2 , 12) B (-3, 6) C (-9, 9)
Post Image Coordinates:
A’ (2, 16) B’ (-4, 8) C’ (-12, 12)
3. Dilate about the origin using a scale
factor of 1
3 .
A (-12, 24) B (-30, 0) C (-36, 36)
Post Image Coordinates:
A’ (-4, 8) B’ (-10, 0) C’ (-12, 12)
4. Dilate about the origin using a scale
factor of 1
2.
A (22, 4) B (8, -4) C (0, 10)
Post Image Coordinates:
A’ (11, 2) B’ (4, -2) C’ (0, 5)
5. Dilate about the origin using a scale
factor of 2.
A (3, -.5) B (3, -2.5) C (0, -4) D (0, -2)
Post Image Coordinates:
A’ (6, -1) B’ (6, -5) C’ (0,-8) D’ (0,-4)
6. Dilate about the origin using a scale
factor of 4.
A (1, -1.5) B (2, -2.5) C (1, -3.5)
Post Image Coordinates:
A’ (4, -6) B’ (8, -10) C’ (4, -14)
7. Dilate about the origin using a scale
factor of 1.
A (0, -8) B (0, -14) C (-5, -14)
Post Image Coordinates:
A’ (0, -8) B’ (0, -14) C’ (-5, -14)
8. Dilate about the origin using a scale
factor of .5
A (-8, 16) B (0, 10)
Post Image Coordinates:
A’ (-4, 8) B’ (0, 5)
Puzzle # 6: Key
Name:_________________________ Date:__________________________
Puzzle # 7: Perform each transformation using
the given pre-image points. Plot the points of the
new image on the provided coordinate plane.
Connect the points in each problem to make a
polygon. When done, you may color your design.
1. Dilate by a scale factor of 2.
A (-1/2, 2.5) B (-.5,- 5.5) C (-4, -1)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
2. Translate Pre Image coordinates
using the rule (y – 10).
A (9, 15) B (-1, 5) C (-1, 15)
Post Image Coordinates:
A’ ________ B’ ________ C’ _________
3. Reflect across the x-axis.
A (-1, 6) B (5, 14) C (-1, 14)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
4. Rotate 90° clockwise about the
origin. A (-2, 12) B (1, 9) C (1, 6) D (-2, 9)
Post Image Coordinates:
A’______B’______ C’_______ D’______
5. Translate 6 left, and 8 up.
A (11, 9) B (16, 3) C (5, 3)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
6. Rotate 90° counter clockwise about
the origin. A (-2, 8) B (-10, 6) C (-15, 9) D (-7, 11)
Post Image Coordinates:
A’______B’______ C’_______ D’______
7. Reflect across the y-axis.
A (-5, 11) B (-5, 5) C (1, 5) D (1, 11)
Post Image Coordinates:
A’______B’______ C’_______ D’______
8. Dilate about the origin by a scale
factor of 1/2.
A (18, 10) B (24, 4) C (12, 4)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
Translations, Reflections, Rotations, Dilations: Horse
1. Dilate by a scale factor of 2.
A (-1/2, 2.5) B (-.5,- 5.5) C (-4, -1)
Post Image Coordinates:
A’ (-1, 5) B’ (-1, -11) C’ (-8, -2)
2. Translate Pre Image coordinates
using the rule (y – 10).
A (9, 15) B (-1, 5) C (-1, 15)
Post Image Coordinates:
A’ (9, 5) B’ (-1, -5) C’ (-1, 5)
3. Reflect across the x-axis.
A (-1, 6) B (5, 14) C (-1, 14)
Post Image Coordinates:
A’ (-1, -6) B’ (5, -14) C’ (-1, -14)
4. Rotate 90° clockwise about the
origin. A (-2, 12) B (1, 9) C (1, 6) D (-2, 9)
Post Image Coordinates:
A’ (12, 2) B’ (9, -1) C’ (6, -1) D’ (9, 2)
5. Translate 6 left, and 8 up.
A (11, 9) B (16, 3) C (5, 3)
Post Image Coordinates:
A’ (5, 17) B’ (10, 11) C’ (-1, 11)
6. Rotate 90° counter clockwise about
the origin. A (-2, 8) B (-10, 6) C (-15, 9) D (-7, 11)
Post Image Coordinates:
A’ (-8, -2) B’ (-6, -10) C’(-9, -15) D’ (-11, -7)
7. Reflect across the y-axis.
A (-5, 11) B (-5, 5) C (1, 5) D (1, 11)
Post Image Coordinates:
A’ (5, 11) B’ (5, 5) C’ (-1, 5) D’ (-1, 11)
8. Dilate about the origin by a scale
factor of 1/2.
A (18, 10) B (24, 4) C (12, 4)
Post Image Coordinates:
A’ (9, 5) B’ (12, 2) C’ (6, 2)
Puzzle # 7:
Key
Name:_________________________ Date:__________________________
Puzzle # 8: Perform each transformation using
the given pre-image points. Plot the points of the
new image on the provided coordinate plane.
Connect the points in each problem to make a
polygon. When done, you may color your design.
1. Reflect over the x-axis, and then
dilate by a scale factor of 1/2.
A (-10, -10) B (6, 4) C (-10, 20)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
2. Rotate 90° clockwise about the
origin, and then dilate using a scale
factor of ¼.
A (16, 44) B (44, 32) C (24, 24)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
3. Translate Pre Image coordinates
using the rule (x - 3) and (y - 1).
A (-3, 12) B (-1, 7) C (-6, 5) D (-8, 10)
Post Image Coordinates:
A’______B’______ C’_______ D’______
4. Rotate 270° counter clockwise about
the origin, and then translate 7 units
up.
A (-6, -1) B (1, -4) C (-4, -6)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
5. Translate 4 left, and then reflect
over the y-axis.
A (1, -2) B (1, -13) C (12, -13)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
6. Translate 5 units down, and then
rotate 90° counter clockwise about
the origin.
A (-6, -1) B (-11, -3) C (-13, 2)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
7. Rotate 180° clockwise about the
origin, and then translate 6 units to
the right.
A (14, -16) B (12, -11) C (17, -9)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
8. Dilate about the origin by a scale
factor of 5.
A (-1, 1) B (-1, -1) C (-2, 0)
Post Image Coordinates:
A’ ________ B’ ________ C’ ________
Mixed Transformations: Cat
1. Reflect over the x-axis, and then
dilate by a scale factor of 1/2.
A (-10, -10) B (6, 4) C (-10, 20)
Post Image Coordinates:
A’ (-5, 5) B’ (3, -2) C’ (-5, -10)
2. Rotate 90° clockwise about the
origin, and then dilate using a scale
factor of ¼.
A (16, 44) B (44, 32) C (24, 24)
Post Image Coordinates:
A’ (11, -4) B’ (8, -11) C’ (6, -6)
3. Translate Pre Image coordinates
using the rule (x - 3) and (y - 1).
A (-3, 12) B (-1, 7) C (-6, 5) D (-8, 10)
Post Image Coordinates: A’ (-6, 11) B’ (-4, 6) C’ (-9, 4) D’ (-11, 9)
4. Rotate 270° counter clockwise about
the origin, and then translate 7
units up.
A (-6, -1) B (1, -4) C (-4, -6)
Post Image Coordinates:
A’ (-1, 13) B’ (-4, 6) C’ (-6, 11)
5. Translate 4 left, and then reflect
over the y-axis.
A (1, -2) B (1, -13) C (12, -13)
Post Image Coordinates:
A’ (3, -2) B’ (3, -13) C’ (-8, -13)
6. Translate 5 units down, and then
rotate 90° counter clockwise about
the origin.
A (-6, -1) B (-11, -3) C (-13, 2)
Post Image Coordinates:
A’ (6, -6) B’ (8, -11) C’ (3, -13)
7. Rotate 180° clockwise about the
origin, and then translate 6 units to
the right.
A (14, -16) B (12, -11) C (17, -9)
Post Image Coordinates:
A’ (-8, 16) B’ (-6, 11) C’ (-11, 9)
8. Dilate about the origin by a scale
factor of 5.
A (-1, 1) B (-1, -1) C (-2, 0)
Post Image Coordinates:
A’ (-5, 5) B’ (-5, -5) C’ (-10, 0)
Puzzle # 8: Key
Name:_________________________ Date:__________________________
Create your own design to give to a friend. Write directions for your transformation moves in each box. List the Pre-Image points. Your friend will write the answers in the space below Post Image Coordinates. Don’t forget to make an answer key.
1.
Post Image Coordinates:
2.
Post Image Coordinates:
3.
Post Image Coordinates:
4.
Post Image Coordinates:
5.
Post Image Coordinates:
6.
Post Image Coordinates:
7.
Post Image Coordinates:
8.
Post Image Coordinates:
Name:_____________________________ Date:____________________
Geometric Transformations
Cheat Sheet: Transformation Rules
1. Translations:
Right-Add to the x coordinate Up- Add to the y coordinate
Left-Subtract from the x coordinate Down- Subtract from the y coordinate
2. Reflections:
Reflecting over the x-axis: change the sign of the y coordinate to its opposite.
Reflecting over the y-axis: change the sign of the x coordinate to its opposite.
3. Rotations About the Origin:
90° 𝐂𝐥𝐨𝐜𝐤𝐰𝐢𝐬𝐞 − Swap the coordinates and change the sign of the new y
coordinate to its opposite.
90° 𝐂𝐨𝐮𝐧𝐭𝐞𝐫 − 𝐂𝐥𝐨𝐜𝐤𝐰𝐢𝐬𝐞 − Swap the coordinates and change the sign of the
new x coordinate to its opposite.
180° 𝐂𝐥𝐨𝐜𝐤𝐰𝐢𝐬𝐞 𝐨𝐫 𝐂𝐨𝐮𝐧𝐭𝐞𝐫 − 𝐂𝐥𝐨𝐜𝐤𝐰𝐢𝐬𝐞 − Do not swap coordinates, just
change the sign of both the x and y
coordinates to their opposites.
270° 𝐂𝐥𝐨𝐜𝐤𝐰𝐢𝐬𝐞 – Do the same as when you rotate 90° Counter-Clockwise.
270° 𝐂𝐨𝐮𝐧𝐭𝐞𝐫 − 𝐂𝐥𝐨𝐜𝐤𝐰𝐢𝐬𝐞 – Do the same as when you rotate 90° Clockwise.
4. Dilations About the Origin:
Multiply both coordinates by the scale factor.