3.1 Sequences of Transformations

Lesson 2: Successive Reflections Across Parallel Lines and its Equivalent

ABC was reflected across the BLUE line to map to A'B'C' which was then reflected across the RED line to map to A''B''C''.

Looking at ABC and A''B''C'', what kind of transformation will map ABC directly to A''B''C''?

Reflection Translation Dilation Rotation

For the LINE angle at 45[sup]o[/sup], what do a and b on the sliders have to be to map ABC to A''B''C''?

a = 3[br]b = -3 a = -3[br]b = -3 a=-3[br]b=3 a = 3[br]b = 3

Notice the vector that emerged from the origin when you moved the 'a' and 'b' sliders. Now use the vector tool to draw vectors from A to A", B to B", and C to C". Do they have the same x and y components as that vector that came out of the origin? What are their components (hint: look at the 'a' and 'b' sliders)?

yes; <3, -3> yes; <0, 0> no; <-3, 3>

Recall that all translations are, in fact, along a vector. This means that the components of the translation vector are built right into the coordinate notation. Now write the transformation in coordinate notation using the values in the previous question.

(x, y) [math]\longrightarrow[/math] (x-3, y-3) (x, y) [math]\longrightarrow[/math] (x+3, y+3) (x, y) [math]\longrightarrow[/math] (x+3, y-3) (x, y) [math]\longrightarrow[/math] (x-3, y+3)

3.1 Sequences of Transformations

Lesson 2: Successive Reflections Across Parallel Lines and its Equivalent

ABC was reflected across the BLUE line to map to A'B'C' which was then reflected across the RED line to map to A''B''C''.

Information: 3.1 Sequences of Transformations