1. Translate, Rotate, Reflect!
A Lesson in Transformations
Professor Davis

2. Translation
A translation is the movement of a figure without turning or reflecting!
So, the figure moves in a direction. Any direction!
But the figure does not turn!

3. Let’s Translate! Watch as the Circle TRANSLATES.
However, be careful! Translations do not always happen in the direction that seems logical!
REMEMBER:
If the figure moves, but does not turn, we call that a translation!
Watch as the Circle TRANSLATES.
The entire figure moves without turning!
BONUS Literacy Note! “trans” at the beginning of a word
usually means “movement”
TRANSport: Movement of an object
TRANSition: Movement between phases
TRANSplant: Movement of an organism

4. Translating on a Graph
Each point of the figure moves the SAME DISTANCE in the SAME DIRECTION in a Translation!
Now... Translate the figure... “3 Units Down”
What is 3 units?
Which direction is down?
Pick some points! We’ll choose the four corners.
Move each of those points down 3 units.
Connect the dots to draw the translated figure.
Check that your points have all moved 3 units!

5. Now, Translate on Your Worksheet!
Problem #1 on your Worksheet
Translate the shaded figure...
4 Units Up
Click to check your answer!
The red diamond is exactly 4 units above the shaded diamond!
Each red brace is four units
[Click to go to the next slide]

6. Reflection
The Line of Reflection is exactly HALFWAY between the Original Figure and the Reflection!
A reflection is when a figure is flipped across a pre-determined “line of reflection”!
In a reflection, each point of the figure moves the same distance to the opposite side of the line of reflection.
The more space between the figure and the line of reflection, the greater distance to the reflection.
The part of the figure that is greatest distance from the line of reflection stays the greatest distance from the line of reflection. The closest part stays closest.
Original Figure
Line of Reflection
Reflected
Figure
Original Figure
Reflected
Figure
Line of Reflection
Line of Reflection
Reflected
Figure

7. Let’s Reflect! Remember...
The distance between the original figure and the Line of Reflection...
Is the SAME as the distance between the reflected figure and the Line of Reflection.
If the original figure is touching the Line of Reflection...
The reflection will be touching the Line of Reflection!
Reflections directly to the left or right of the original figure are also the same shape!
Reflections directly above the figure and directly below the figure are the same shape!
The part of the figure closest to the Line of Reflection will stay the closest part after the reflection.
In this triangle, the longest side is the closest to the Line of Reflection. This is true in both the original figure, and the reflection.

8. Guess the Reflection! Problem #2 On Your Worksheet
Guess the Reflection by drawing the
Reflected Shape on your Paper!
(Click to see if you were correct!)
Problem #3 On Your Worksheet
[Click to continue to the next slide]

9. Reflecting on a Graph
Each point on the figure is the same distance from the LINE OF REFLECTION.
Now... Reflect the Figure... Across the Line of Reflection
Find the Line of Reflection
Measure the distance of a point from the Line of Reflection
Draw a point that same distance, in the other direction from the line
Repeat for more points
Connect the dots!
Line of Reflection

10. Now, Reflect on Your Worksheet!
Problem #4 on your Worksheet
Reflect the Figure Across the Dotted Line
Find the Line of Reflection
Measure the distance of a point on the edge of the figure, to the Line of Reflection
Draw a point that same distance, in the other direction from the line
Repeat for more points
Connect the dots
Click to check your answer!
[Click to continue to the next slide]

11. Draw the Line of Reflection!
Problem #7 on your Worksheet
Problem #8 on your Worksheet
Problem #6 on your Worksheet
Problem #5 on your Worksheet
You will see two figures. One is shaded, and one has dots.
Draw the Line of Reflection!
Remember, the Line of Reflection is the SAME DISTANCE from both figures!
After you draw a line, measure to both figures to check your answer!
Click to see the correct answer!
[Click to continue to the next slide]

12. Rotation
In a Rotation, the Center Point stays in the same place, and every other part of the figure moves.
The farther a point is from the center of the figure, the further it moves.
Literacy BONUS Note! “fUrther” is used for Comparisons of Two Things
“fArther” is used with Distance Words
So...
“farther a point is from the center” is distance!
“further [the point] moves” is a comparison!

13. Describing Rotations Clockwise
Rotations are most often described by the terms “Clockwise” or “Counter-Clockwise”.
Clockwise

14. Describing Rotations Counter-Clockwise
Rotations are most often described by the terms “Clockwise” or “Counter-Clockwise”.
Counter-Clockwise

15. Let’s Rotate! Quarter Rotation, Clockwise Quarter Rotation,
Counter-Clockwise
Half-Rotation,
Counter-Clockwise
Half-Rotation,
Clockwise

16. Rotating on a Graph
In a Rotation, the Center Point stays in the same place, and every other part of the figure moves.
After rotating on a graph, make sure the edges of the figure are the same distance from the center point [to be sure the figure has not been stretched, shrunk, or reshaped].
In this case, the edges of the figures are 3 units from the center.
3 Units from center to edge
3 Units from center to edge
Center Point

17. Name the Transformation!
Problem #11
Problem #10
Problem #9 On Your Worksheet
Figure A
Name the Transformation that occurred between Figure A [The Original Figure] and Figure B [The Transformation].
Translation
Reflection
Rotation
No Transformation
[Click to check your answer!]
Figure B