1.6 what if it is reflected more than once? pg. 26 rigid transformations: translations

1.6

What if it is Reflected More than Once?

Pg. 26Rigid Transformations: Translations

1.6 – What if it is reflected more than Once?_____Rigid Transformations: Translations

In Lesson 1.5, you learned how to change a shape by reflecting it across a line, like the ice cream cones shown at right. Today you will learn more about reflections and learn about two new types of transformations: translations.

1.32 – TWO REFLECTIONS As Amanda was finding reflections, she wondered, “What if I reflect a shape twice over parallel lines?” Investigate her question as you answer the questions below.

a. Find ∆ABC and lines n and p (shown below). What happens when ∆ABC isreflected across line n to form and then is reflected across line p to form First visualize the reflections and then test your idea of the result by drawing both reflections.

Prediction

Drawing

'A

'B 'C

''A

''B''C

b. Examine your result from part (a). Compare the original triangle ∆ABC with the final result, What single motion would change ∆ABC to

'' '' ''.A B C'' '' ''?A B C

Moving it over, sliding

c. Amanda analyzed her results from part (a). “It Just looks like I could have just slid ∆ABC over!” Sliding a shape from its original position to a new position is called translating. For example, the ice cream cone at right has been translated. Notice that the image of the ice cream cone has the same orientation as the original (that is, it is not turned or flipped). What words can you use to describe a translation?

Moving it over, sliding

d. The words transformation and translation sound alike and can easily be confused. Discuss in your team what these words mean and how they are related to each other.

Transformation:

Translation:

Moving the shape in some way

Sliding shape over

1.33 – TRANSLATIONS ON A GRID The formal name for a slide is a translation. (Remember that translation and transformation are different words.) at right is the result of translating .ABC

a. Describe the translation. That is, how many units to the right and how many units down does the translation move the triangle?

Right 7

Down 3

, 7, 3x y x y Right 7 Down 3

c. On graph paper, plot if E(-3, 4), F (-6, 6), and G(-3, 0). Find the coordinates of if is translated the same way as was in part (a).

EFG

ABC

EF

G

ERight 7

Down 3

c. On graph paper, plot if E(-3, 4), F (-6, 6), and G(-3, 0). Find the coordinates of if is translated the same way as was in part (a).

EFG

ABC

EF

G

'E'F

'G

Right 7

Down 3

d. is the result of performing the same translation on If (2, -3), (4, -5), and (5, 1), name the coordinates of X, Y, and Z.

'X 'Y'Z

' ' 'X Y Z

'X

'Z

'Y

'X

Right 7

Down 3

Left 7

Up 3

d. is the result of performing the same translation on If (2, -3), (4, -5), and (5, 1), name the coordinates of X, Y, and Z.

'X 'Y'Z

' ' 'X Y Z

'X

'Z

'Y

Right 7

Down 3

Left 7

Up 3

X

Z

Y

e. What movement would occur with the following rules:

, 4, 1x y x y Left 4 Up 1

e. What movement would occur with the following rules:

down 5

, , 5x y x y

e. What movement would occur with the following rules:

Right 8

, 8,x y x y