Answer:
Option A is correct
The only figure after composition of [tex]t_{0 , 3} (r_{0,90^{\circ}})[/tex] to figure R is Figure H
Step-by-step explanation:
From the given figure in R;
The coordinates in Figure R ;
(1 , -1) , (2, -2) ,(4, -2) ( 0, -4)
Composite function defined as when one function is substituted into another function.
To Apply the composition [tex]t_{0 , 3} (r_{0,90^{\circ}})[/tex] to figure R;
First apply the Reflection [tex]r_{0, 90^{\circ}}[/tex] in Figure R;
The rule of reflection is given by:
[tex](x,y) \rightarrow (-y,x)[/tex]
By applying the rule of reflection in Figure R ,
then, the coordinates becomes;
(1 , -1) [tex]\rightarrow[/tex] (1, 1)
(2 , -2) [tex]\rightarrow[/tex] (2, 2)
(4 , -2) [tex]\rightarrow[/tex] (2, 4)
(0, -4) [tex]\rightarrow[/tex] (4, 0)
Now, apply the translation [tex]t_{0,3}[/tex]
Translation : It is a type of transformation that moves each point in a figure the same distance in the same direction.
then,
the rule of translation is:
[tex](x,y) \rightarrow (x+0,y+3)[/tex]
Apply the rule of translation on coordinates (1,1) , (2,2), (2,4) and (4,0)
then
(1 , 1) [tex]\rightarrow[/tex] (1+0 1+3) =(1,4)
(2, 2) [tex]\rightarrow[/tex] (2+0 2+3) =(2, 5)
(2, 4) [tex]\rightarrow[/tex] (2+0 4+3) =(2 ,7) and
(4, 0) [tex]\rightarrow[/tex] (4+0 0+3) =(4 ,3)
Then, the only figure after composition of [tex]t_{0 , 3} (r_{0,90^{\circ}})[/tex] to figure R is Figure H
