Lesson 3 Can You Get There From Here? Develop Understanding

Ready

The given figures are to be used as pre-images. Perform each transformation to obtain an image. Label the corresponding parts of the image as described.

1.

Reflect triangle $A B C$ over the line $y = x$ , and label the image $A^{'} B^{'} C^{'}$ .
Rotate triangle $A^{'} B^{'} C^{'}$ $180 °$ counterclockwise around the origin, and label the image $A^{″} B^{″} C^{″}$ .

2.

Reflect over the line $y = - x$ .

3.

Reflect over the $y$ -axis, and then rotate clockwise $90 °$ around $P^{'}$ .

4.

Reflect quadrilateral $A B C D$ over the line $y = 2 + x$ , and label the image $A^{'} B^{'} C^{'} D^{'}$ .

Rotate quadrilateral $A^{'} B^{'} C^{'} D^{'}$ counterclockwise $90 °$ around $(- 2, - 3)$ as the center of rotation. Label the image $A^{″} B^{″} C^{″} D^{″}$ .

Set

Find a sequence of transformations that will carry triangle $R S T$ onto triangle $R^{'} S^{'} T^{'}$ .

Clearly describe the sequence of transformations.

5.

6.

7.

Even though there are many possible sequences of transformations that could be used to place one figure on top of another, there is one sequence that is logically more efficient than the others. (This would have been discussed in class today.) What is the reliable sequence of transformations that can be used every time you need to describe a transformation?

Go

Graph each pair of functions, and make an observation about how the functions compare to one another.

8.

$\begin{matrix} y = \frac{1}{3} x - 1 \\ y = - 3 x - 1 \end{matrix}$

9.

$\begin{matrix} y = - \frac{2}{3} x + 5 \\ y = \frac{3}{2} x + 5 \end{matrix}$

10.

$\begin{matrix} y = \frac{1}{4} x + 2 \\ y = - \frac{1}{4} + 2 \end{matrix}$

11.

$\begin{matrix} y = 2^{x} \\ y = - 2^{x} \end{matrix}$