1. Translations Translations maintain Same Size Same Shape
Same Orientation
∆ABC → ∆A’B’C’
A → A’
B → B’
C → C’ A B C A’ B’ C’
y + 2
(x,y)
x + 6
( x, y ) → ( x + 6, y + 2 )
( - 3,1) → ( , ) B
B’ ( 3, 3)

2. Translations Translations maintain Same Size Same Shape
Same Orientation
∆ABC → ∆A’B’C’
A → A’
B → B’
C → C’ A B C
x + 8 A’ B’ C’
(x,y)
y – 5
( x, y ) → ( x + 8, y – 5 )
( - 5,4) → ( , 4 – 5 ) A
A’ ( 3, -1)

3. Reflections • • • Reflections maintain Same Size Same Shape
Reflection is over a line
The Orientation of the new image is a mirror image of the original
A (-3,4)
A’ (3,4) • • •
B (-3,1) C
(-1,1) C’
(1,1)
B’ (3,1)
Reflection over the y-axis
Any point, A, reflected over a line to A’
is the same distance on the opposite side of the line

4. Reflections • • • Reflections maintain Same Size Same Shape
Reflection is over a line
The Orientation of the new image is a mirror image of the original
A (-3,4) •
Reflection over the x-axis
Any point, A, reflected over a line to A’
is the same distance on the opposite side of the line • •
C (-1,1)
B (-3,1)
C’ (-1,-1)
B’ (-3,-1)
A’ (-3,-4)

5. Reflections • • • Reflections maintain Same Size Same Shape
Reflection is over a line
The Orientation of the new image is a mirror image of the original
A (-3,4) •
Reflection over the line y = x
Any point, A, reflected over a line to A’
is the same distance on the opposite side of the line • •
C (-1,1)
B (-3,1)
C’ (1,-1) B’
(1, -3)
A’ (4, -3)

6. Rotations • • • Rotations maintain Same Size Same Shape
Rotation is around a point
A’ and A are both the same distance from center of rotation.
A (-5,4) • • •
90° counter-clockwise rotation about the origin
Positive 90°
B (-5,1)
C (-3,1)
C’ (-1, -3)
A’ (-4, -5)
B’ (-1, -5)

7. Rotations • • • Rotations maintain Same Size Same Shape
Rotation is around a point
A’ and A are both the same distance from center of rotation.
B’ (1, 5)
A’ (4, 5)
A (-5,4) •
C’ (1, 3) • •
B (-5,1)
C (-3,1)
90° clockwise rotation about the origin
Negative 90°

8. Rotations • • • Rotations maintain Same Size Same Shape
Rotation is around a point
A’ and A are both the same distance from center of rotation.
A (-5,4) •
180° counter-clockwise rotation about the origin
Positive 180° • •
B (-5,1)
C (-3,1)
C’ (3, -1)
B’ (5, -1)
A’ (5, -4)

9. Dilation
A Dilation causes a change in size but not a change in shape.
The points move along lines drawn from the center of dilation through the original points.
The scale factor is the ratio of a side of the new figure to the corresponding side of the original figure.
A (4, 8)
A (2, 4) •
B (4, 2)
C (8, 2) • •
B (2, 1)
C (4, 1) •
Dilation with the Center at the origin and a scale factor of 2

10. Dilation
A Dilation causes a change in size but not a change in shape.
The points move along lines drawn from the center of dilation through the original points.
The scale factor is the ratio of a side of the new figure to the corresponding side of the original figure.
A (3, 6) •
A’ (2, 4)
B (3, 3) • •
C (9, 3)
B ‘(2, 2)
C (6, 2) •
Dilation with the Center at the origin and a scale factor of / 3.