1. 9-1: Reflections

2. Definitions preimage-the shape before it is transformed.
reflection-a transformation representing a flip of a figure.
isometry-when the result of a transformation and its preimage are congruent.
A reflection is an isometry.

3. You can reflect an image about a line or a point.
The main reflections we will consider are:
Lines
Reflection over x-axis
Reflection over y-axis
Reflection over y=x
Point – reflection over origin.

4. Reflect point A over the x-axis.
What changes about the coordinates of the points?

5. Reflect point B over the y-axis.
What changes about the coordinates of the points?

6. Reflect point C over the origin.
What changes about the coordinates of the points?

7. Reflect point D over the line y=x.
What changes about the coordinates of the points?

8. Reflection
Preimage to image
Example
x-axis
(a,b) →(a,-b)
A=(3,2)
A’=(3,-2)
y-axis
(a,b) →(-a,b)
B=(4,5)
B’=(-4,5)
origin
(a,b) →(-a,-b)
C=(-2,-5)
C’=(2,5)
y=x
(a,b) →(b,a)
D=(4,7)
D’=(7,4)

9. Reflect the point A(4,5) over the x-axis.
Reflect the triangle with A(-2,1), B(3,4) and C(0,7) over the origin.
Reflect the square with A(3,0), B(3,3), C(0,3) and D(0,0) over the line y=x.

10. Symmetry
Line of symmetry – when you fold the shape over this line the two halves match exactly.
EX:
Point of symmetry – a point that is a common point of reflection for all points on a figure.

11. How to write coordinates as a matrix.
The dimensions of your matrix will always be (2 x # of points)
x-values go in the first row
y-values go in the bottom row
EX: Write a vertex matrix for quadrilateral ABCD with
A(2,3)
B(-4,5)
C(-5,-2)
D(0,-2)

12. Reflection matrices
x-axis→
y-axis →
origin →
y=x →

13. Use the reflection matrices to reflect the pentagon with the following vertex matrix over the…
1. x-axis y-axis

14. Reflect the following shape about the line y=x.

15. Assignment
WB 9-1
Worksheet 9-1