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1.6What if it is Reflected More than Once?Pg. 23Rigid Transformations: Translations1.6 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 a new type of transformation: translations.

1.38 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.PredictionDrawing

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

Moving it over, slidingGeogebra Reflectionsc. 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, slidingTranslationTransformationMoving the shape in some waySliding shape over

TranslationSlid over, not flipped

Right 7Down 3Motion Rule:

Rightor LeftUpor Down

Right 7Down 3

Left 4Up 1Right 3Down 7Down 5Right 8

+43

5+6

87

(2, 3)(-1, 5)(2, -1)

(-2, -2)(2, -1)(4, -5)

f. Can you find the new point without counting on the graph? Use the motion rule to find if P is at (2, -1).

(2 3, -1 + 1)

(2 + 7, -1 3)

(2 + 5, -1)

1.40 NON-CONGRUENT RULES Use the following rules to find the new shape by plugging in each x and y value to find the new coordinate.

(-1, -4)(0, -2)(3, -4)

(-6, -4)(-4, -2)(2, -4)

c. What is the difference between (a) and (b)? Why do you think one is congruent to the original and one is not?

Multiplying changes the size of the shape1.41 WORKING BACKWARDS What if you are only given the location of the translated shape? Can you find the original shape?

Right 4Down 1Left 4Up 1

(-2, -2)(0, -4)(1, 2)

Left 3Right 3

(6, -1)(6, -4)(4, -4)