Answer:
[tex]A" = (-1,-3)[/tex] [tex]B" = (-2,-6)[/tex] [tex]C" = (1,-7)[/tex]
Step-by-step explanation:
Given
See attachment for graph
[tex]A' = (-4, -5)[/tex]
[tex]B'=(-5, -2)[/tex]
[tex]C' = (-2, -1)[/tex]
First, reflect over [tex]y =-4[/tex]
The rule is: [tex](x,y) ==> (x,y+h)[/tex]
Where [tex]h =-4[/tex]
So:
[tex]A' = (-4, -5)[/tex] [tex]==>[/tex] [tex]A'' = (-4, 1-4) = (-4, -3)\\[/tex]
[tex]B'=(-5, -2)[/tex] [tex]==>[/tex] [tex]B'' = (-5, -2-4) = (-5, -6)[/tex]
[tex]C' = (-2, -1)[/tex] [tex]==>[/tex] [tex]C'' = (-2, -3-4) = (-2, -7)[/tex]
So, we have:
[tex]A" = (-4,-3)[/tex] [tex]B" = (-5,-6)[/tex] [tex]C" = (-2,-7)[/tex]
Next translate A''B''C'' by T(3, 0), we have;
The rule is: [tex](x,y)==>(x+3,y+0)[/tex]
[tex]A" = (-4,-3)[/tex] [tex]==>[/tex] [tex]A" = (-4 + 3, -3+0) = (-1, -3)[/tex]
[tex]B" = (-5,-6)[/tex] [tex]==>[/tex] [tex]B" = (-5 + 3, -6) = (-2, -6)[/tex]
[tex]C" = (-2,-7)[/tex] [tex]==>[/tex] [tex]C" = (-2 + 3, -7) = (1 , -7)[/tex]
Hence, A''B''C'' are:
[tex]A" = (-1,-3)[/tex] [tex]B" = (-2,-6)[/tex] [tex]C" = (1,-7)[/tex]
