B Apply

Geometry Each matrix represents the vertices of a polygon. Translate each figure 5 units left and 1 unit up. Express your answer as a matrix.

26. [ − 3 − 3 2 2 − 2 − 4 − 2 − 4 ] . matrix with 2 rows and 4 columns , row1 column 1 , negative 3 , column 2 negative 3 , column 3 2 , column 4 2 , row2 column 1 , negative 2 , column 2 negative 4 , column 3 negative 2 , column 4 negative 4 , end matrix
27. [ − 3 0 3 0 − 9 − 6 − 9 − 12 ] . matrix with 2 rows and 4 columns , row1 column 1 , negative 3 , column 2 0 , column 3 3 , column 4 0 , row2 column 1 , negative 9 , column 2 negative 6 , column 3 negative 9 , column 4 negative 12 , end matrix
28. [ 0 1 − 4 0 3 5 ] . matrix with 2 rows and 3 columns , row1 column 1 , 0 , column 2 1 , column 3 negative 4 , row2 column 1 , 0 , column 2 3 , column 3 5 , end matrix

For Exercises 29–32, use Δ A B C . cap delta eh b c . Write the coordinates of each image in matrix form.

29. a translation 2 units left and 3 units down
30. a dilation half the original size
31. a rotation of 180 ° 180 degrees
32. a reflection across the x-axis
33. Think About a Plan In an upcoming cartoon, the hero is a gymnast. In one scene he swings around a high bar. Describe the rotation matrices that would be needed so four frames of the movie would show the illustrated motion (below), one frame after the other.
    • What do you need to do first to describe the motion?

    • Can you use just one rotation matrix, or do you need three?

      Frame 1	Frame 2	Frame 3	Frame 4

34. Animation Suppose you want the cartoon of the gymnast in the previous exercise to show two revolutions around the bar. What rotation matrices are needed so eight frames of the movie would show the illustrated motion, one frame after the other.
35. Writing Explain why you might want to represent a transformation as a matrix.

Use matrices to represent the vertices of graph f and graph g. Name each transformation.

36. 
    Image Long Description
37. 
    Image Long Description
38. 
    Image Long Description

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