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1. Transformational
Geometry

2. Definitions of
Transformations

3. Translation
The transformation of moving an object a certain distance.
The object stays the exact same, not having been reflected, rotated or re-sized.
Every point of the object moves in the same direction, and the same distance.

4. How to Perform a Translation (Directions)
1. Pinpoint the X and Y location to translate
the object to.
2. First, begin with the X axis, which is
horizontal on the Cartesian Graph.
3. Count a certain amount of spaces on the X
axis, and then mark the position.
4. Next, continue with the Y axis, which is
vertical on the Cartesian Graph.
5. Count a certain amount of spaces, and then
mark the position.
6. Line up both markings and draw the shape
from the point it was translated.

5. How to Perform a Translation (Link)
(Click on Image)

6. Rotation
The transformation in which an object is turned around a fixed point.
One point of the object is fixed.
The rest of the object pivots around the fixed point at any given angle.

7. 1. Mark a point to rotate an
object around.
2. Choose an angle, up to 359o,
as well as clockwise, or counter
clockwise.
3. Rotate the object at the
previously chosen angle.
4. Redraw the object to the exact
same size.
How to Perform a Rotation (Directions)

8. How to Perform a Rotation (Link)
(Click on Image)

9. The transformation in which a geometric figure is mirrored across a line
Which creates a mirror image.
The line that mirrors the figure is called the axis of reflection.
Reflection

10. 1. Pinpoint an axis of
reflection.
2. Calculate how far away
your object is from your
axis of reflection.
3. Redraw your object the
same distance away, but
have it symmetrical.
How to Perform a Reflection (Directions)

11. How to Perform a Reflection (Link)
(Click on Image)

12. 1. Translate a 2x1 unit
rectangle by point D from
-2, 4 to 3, -4.
2. Reflect the rectangle
across the axis of
reflection provided.
3. Rotate the rectangle
clockwise 180o at point D
Transformation Question
D
BA
C
-1
-2
-3
-4
-5
-5 -4 -3 -2 -1
5
4
3
2
1
1 2 3 4 5
Axis of Reflection

13. D
BA
C
-1
-2
-3
-4
-5
-5 -4 -3 -2 -1
5
4
3
2
1
1 2 3 4 5
Solution - Step One: Translation
D
BA
C
-1
-2
-3
-4
-5
-5 -4 -3 -2 -1
5
4
3
2
1
1 2 3 4 5
Axis of Reflection

14. Solution - Step Two: Reflection
-1
-2
-3
-4
-5
-5 -4 -3 -2 -1
5
4
3
2
1
1 2 3 4 5
Axis of Reflection
D
BA
C
-1
-2
-3
-4
-5
-5 -4 -3 -2 -1
5
4
3
2
1
1 2 3 4 5
Axis of Reflection
D
BA
C

15. Solution - Step Three: Rotation
-1
-2
-3
-4
-5
-5 -4 -3 -2 -1
5
4
3
2
1
1 2 3 4 5
Axis of Reflection
D
BA
C
-1
-2
-3
-4
-5
-5 -4 -3 -2 -1
5
4
3
2
1
1 2 3 4 5
Axis of Reflection
D B
AC

16. /
The End