1. Transformations with Matrices
Chapter 4, Section 4

2. Writing ordered pairs as matrices:
To write ordered pairs as a matrix, put the x values in row 1 and the y-values in row 2
(2,3) (4,5) (-1,8) (5,10)
(-1,2) (3,4) (8,0)
**original points are called the preimage, new points are called the image

3. Types of Transformations
Translations – figure is moved up, down, left, or right
Size, shape, and orientation do NOT change
Dilations – figure changes size
Shape and position do NOT change

4. Types of Transformations
Reflections – figure is flipped over a line of symmetry
Size and shape do NOT change
Lines of reflections: y-axis, x-axis, line y=x
Rotations – figure is moved around a center point
Degrees of rotations: 90, 180, 270

5. Some vocabulary:
Vertex matrix – a matrix that consists of the original ordered pairs.
Translation matrix – a matrix that shows how the figure is translated. *Will be the same size as vertex matrix*

6. Translations Step 1: Vertex Matrix Step 2: Translation Matrix
Step 3: add the vertex matrix and the translation matrix together to get the new matrix
Step 4: write the new ordered pairs from the new matrix – this is the answer 6

7. Translation Example
Translate triangle ABC 3 units left and 4 units up with vertices A(2, 3), B(-1, 4), C(0, 5) 7

8. Dilations Step 1: Vertex Matrix Step 2: determine the scale factor
Step 3: multiply the scale factor by the vertex matrix to get the new matrix
Step 4: write the new ordered pairs from the new matrix – this is the answer

9. Dilation Example
Find the coordinates of triangle ABC if the perimeter of triangle ABC is reduced by ½ with vertices A(2, 3), B(-1, 4), C(0, 5) 9

10. Reflections Step 1: determine what line the figure is reflected over
Step 2: change the coordinates based on the line of reflection
Step 3: write the new ordered pairs 10

11. Demonstrating a Reflection

12. Demonstrating a Reflection - Conclusions
When reflected over the x-axis:
change the sign of the y values
When reflected over the y-axis:
change the sign of the x values
When reflected over the line y=x:
switch the x and y values

13. Rotations Step 1: determine the degree to rotate the figure
Step 2: change the coordinates based on the degree of rotation
Step 3: write the new ordered pairs
**all rotations will be performed counter-clockwise 13

14. Demonstrating a Rotation

15. Demonstrating a Rotation- Conclusions
When rotated 90 degrees:
switch the x and y values and change the sign of the new x values
When rotated 180 degrees:
change the sign of the x and y values
When rotated 270 degrees:
switch the x and y values and change the sign of the new y values

16. Your turn: Classwork: Homework:
4-4 in practice workbooks.
Homework:
Transformations handout
Exit Slip:Describe each of the transformations using only 1 word for each one.