4.1 Review Worksheet (continued)
Use the following matrices for Exercises 23-32. Simplify, if possible.
2 1 0 2 0 1 1 2 1
− 0 1 1 4 2 3
= C
= T
− 1 1 1 1
1 2 1 0
2 1 3 0 3 5
−
− 4 13 9
= S
Q
A
B
=
=
−
=
−
23. S 2
24. B 2
25. T 2
26. S 3
27. Q 3
28. AB
29. BA
30. 2 BA − C
31. 3 CB + 2 B
32. ( BA ) 2
4.1.3 Using Matrices to Transform Geometric Figures 33. Translate the polygon with coordinates D (0, 4), E ( − 3, − l), F (l, − 5) and G (l, 0) 3 units right and 3 units up. Find the coordinates of the vertices of the image, and graph.
34. Dilate the polygon with coordinates W (1, 2), X ( − 2, 3), Y ( − 3, 4), and Z ( − 4, 1) by a factor of 3 2 . Find the coordinates of the vertices of the image, and graph.
35. Reflect the figure with coordinates A ( − 2, 3), B (0, 4), C (2, 3), D (2, l), and E ( − 1, − 1) across the x -axis. Graph and describe the image.
Use each matrix to rotate the figure PQRST with coordinates P (–3, 2), Q (0, 0), R (–4, 1), S (–4, 4), and T (–1, 4). Graph and describe the image. 36. − 37.
y
S
T
P
0 1 1 0
0 1 1 0
2
−
x
Q
R
0
–4 –2
2
4
–2
–4
206
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