Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Use matrix addition to find the coordinates of each image after a translation 3 units left and 5 units up. If possible, graph each pair of figures on the same coordinate plane.

7. A ( 1 , − 3 ) , eh open 1 comma negative 3 close comma  B(1, 1), C(5, 1), D ( 5 , − 3 ) d open 5 comma negative 3 close
8. G(0, 0), H(4, 4), I(8, 0), J ( 4 , − 4 ) j open 4 comma negative 4 close
9. J ( − 10 , 2 ) , K ( − 16 , 1 ) , L ( 12 , − 5 ) open negative 10 comma 2 close comma k open negative 16 comma 1 close comma l open 12 comma negative 5 close
10. R(9, 3), S(3, 6), T(3, 3), U ( 6 , − 3 ) u open 6 comma negative 3 close

See Problem 2.

Find the coordinates of each image after the given dilation.

11. [ 0 2 5 8 0 4 5 1 ] , 2 . matrix with 2 rows and 4 columns , row1 column 1 , 0 , column 2 2 , column 3 5 , column 4 8 , row2 column 1 , 0 , column 2 4 , column 3 5 , column 4 1 , end matrix . comma 2
12. [ − 7 − 3 4 − 5 4 0 ] , 0.5 . matrix with 2 rows and 3 columns , row1 column 1 , negative 7 , column 2 negative 3 , column 3 4 , row2 column 1 , negative 5 , column 2 4 , column 3 0 , end matrix . comma 0.5
13. [ − 8 2 3 1 − 2 6 4 0 − 4 0 ] , 1 . 5 . matrix with 2 rows and 5 columns , row1 column 1 , negative 8 , column 2 2 , column 3 3 , column 4 1 , column 5 negative 2 , row2 column 1 , 6 , column 2 4 , column 3 0 , column 4 negative 4 , column 5 0 , end matrix . comma 1 . 5

See Problem 3.

Graph each figure and its image after the given rotation.

14. [ 0 − 3 5 0 1 2 ] ; 90 ° . matrix with 2 rows and 3 columns , row1 column 1 , 0 , column 2 negative 3 , column 3 5 , row2 column 1 , 0 , column 2 1 , column 3 2 , end matrix . semicolon . 90 to the degrees
15. [ − 1 0 5 − 1 5 0 ] ; 180 ° . matrix with 2 rows and 3 columns , row1 column 1 , negative 1 , column 2 0 , column 3 5 , row2 column 1 , negative 1 , column 2 5 , column 3 0 , end matrix . semicolon . 180 to the degrees
16. [ − 5 6 0 − 1 2 4 ] ; 90 ° . matrix with 2 rows and 3 columns , row1 column 1 , negative 5 , column 2 6 , column 3 0 , row2 column 1 , negative 1 , column 2 2 , column 3 4 , end matrix . semicolon . 90 to the degrees

Find the coordinates of each image after the given rotation.

17. [ 3 6 3 6 − 3 3 3 − 3 ] ; 270 ° . matrix with 2 rows and 4 columns , row1 column 1 , 3 , column 2 6 , column 3 3 , column 4 6 , row2 column 1 , negative 3 , column 2 3 , column 3 3 , column 4 negative 3 , end matrix . semicolon . 270 degrees
18. [ 0 4 8 6 0 4 4 2 ] ; 360 ° . matrix with 2 rows and 4 columns , row1 column 1 , 0 , column 2 4 , column 3 8 , column 4 6 , row2 column 1 , 0 , column 2 4 , column 3 4 , column 4 2 , end matrix . semicolon . 360 degrees
19. [ 1 2 3 4 2.5 3 2 2 3 5 ] ; 180 ° . matrix with 2 rows and 5 columns , row1 column 1 , 1 , column 2 2 , column 3 3 , column 4 4 , column 5 2.5 , row2 column 1 , 3 , column 2 2 , column 3 2 , column 4 3 , column 5 5 , end matrix . semicolon . 180 degrees

See Problem 4.

Graph each figure and its image after reflection across the given line.

20. [ 0 − 3 5 0 1 2 ] ; y = x . matrix with 2 rows and 3 columns , row1 column 1 , 0 , column 2 negative 3 , column 3 5 , row2 column 1 , 0 , column 2 1 , column 3 2 , end matrix . semicolon y equals x
21. [ − 1 0 5 − 1 5 0 ] ; . matrix with 2 rows and 3 columns , row1 column 1 , negative 1 , column 2 0 , column 3 5 , row2 column 1 , negative 1 , column 2 5 , column 3 0 , end matrix . semicolon  y–axis
22. [ − 3 − 5 − 10 4 7 1 ] ; . matrix with 2 rows and 3 columns , row1 column 1 , negative 3 , column 2 negative 5 , column 3 negative 10 , row2 column 1 , 4 , column 2 7 , column 3 1 , end matrix . semicolon  x–axis

Find the coordinates of each image after reflection across the given line.

23. [ 3 6 3 6 − 3 3 3 − 3 ] ; y = − x . matrix with 2 rows and 4 columns , row1 column 1 , 3 , column 2 6 , column 3 3 , column 4 6 , row2 column 1 , negative 3 , column 2 3 , column 3 3 , column 4 negative 3 , end matrix . semicolon y equals negative x
24. [ 0 4 8 6 0 4 4 2 ] ; . matrix with 2 rows and 4 columns , row1 column 1 , 0 , column 2 4 , column 3 8 , column 4 6 , row2 column 1 , 0 , column 2 4 , column 3 4 , column 4 2 , end matrix . semicolon  x–axis
25. [ 1 2 3 4 2.5 3 2 2 3 5 ] ; y = x . matrix with 2 rows and 5 columns , row1 column 1 , 1 , column 2 2 , column 3 3 , column 4 4 , column 5 2.5 , row2 column 1 , 3 , column 2 2 , column 3 2 , column 4 3 , column 5 5 , end matrix . semicolon y equals x

Table of Contents