Question

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

A.


figure H




B.


figure I




C.


figure J




D.


figure R

Answer 1

The correct answer is choice A) Figure H

Answer 2

Option A is correct

The only figure after composition of
`t_(0 , 3) (r_(0,90^(\circ)))` to figure R is Figure H

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