1. COMPOSITIONS WITH TRANSFORMATIONS

2. COMPOSITIONS Definition: The nesting of two or more processes to form a single new rule. Composition of Transformations When two transformations are performed, one following the other. Notation: Perform the transformations from right to left T a,b o r y=x (x,y)

3. COMPOSITIONS PRACTICE Find the image of A(3,-2) under the given compositions. R 90° ∘ r x-axis r x-axis (3, -2) => (3, 2) R 90° (3, 2) => (-2, 3)

4. COMPOSITIONS PRACTICE What happens if we reverse them? Find the image of A(3,-2) under the given compositions. r x-axis ∘ R 90° R 90° (3, -2) => (2, 3) r x-axis (2, 3) => (2, -3)

5. COMPARE R 90° ∘ r x-axis = (-2, 3) r x-axis ∘ R 90° = (2, -3) ORDER MATTERS!!

6. FIND THE IMAGE OF A(3,-2) UNDER THE GIVEN COMPOSITIONS. 1.r x-axis ∘ r y-axis 2.r y-axis ∘ r x-axis 3.R 90 ∘ r x-axis 4.r y-axis ∘ R 90 5.T -1,4 ∘ r y=x 6.r y=x ∘ R 90 7.r y-axis ∘ r y=x 8.R 90 ∘ T 3,-2 9.T -2,4 ∘ D -2 10.D -2 ∘ T -2,4