Question

Which figure is the image produced by applying the composition t 0,3 r 0,90 to figure R?

Answer 1

Answer:

Option A is correct

The only figure after composition of $t_{0 , 3} (r_{0,90^{\circ}})$ 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 $t_{0 , 3} (r_{0,90^{\circ}})$ to figure R;

First apply the Reflection $r_{0, 90^{\circ}}$ in Figure R;

The rule of reflection is given by:

$(x,y) \rightarrow (-y,x)$

By applying the rule of reflection in Figure R ,

then, the coordinates becomes;

(1 , -1) $\rightarrow$ (1, 1)

(2 , -2) $\rightarrow$ (2, 2)

(4 , -2) $\rightarrow$ (2, 4)

(0, -4) $\rightarrow$ (4, 0)

Now, apply the translation $t_{0,3}$

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:

$(x,y) \rightarrow (x+0,y+3)$

Apply the rule of translation on coordinates (1,1) , (2,2),  (2,4) and (4,0)

then

(1 , 1) $\rightarrow$ (1+0 1+3) =(1,4)

(2, 2) $\rightarrow$ (2+0 2+3) =(2, 5)

(2, 4) $\rightarrow$ (2+0 4+3) =(2 ,7) and

(4, 0) $\rightarrow$ (4+0 0+3) =(4 ,3)

Then, the only figure after composition of $t_{0 , 3} (r_{0,90^{\circ}})$ to figure R is Figure H

Answer 2

Answer:

The correct answer is choice A) Figure H