Question

The figure shows the letter Z and four of its transformed images—A, B, C, and D:

Which of the following rules will transform the pre-image of Z in quadrant 2 into its image in quadrant 1?

a.( x , y ) ⟶ ( − y , − x )

b. ( x , y ) ⟶ ( x , − y )

c. ( x , y ) ⟶ ( − x , y )

d. ( x, y ) ⟶ ( - x, -y )

Answer 1

Given:

The figure shows the letter Z and four of its transformed images—A, B, C, and D.

To find:

Which of the following rules will transform the pre-image of Z in quadrant 2 into its image in quadrant 1?

Solution:

From the figure it is clear that the pre-image of Z in quadrant 2 and its image in quadrant 1 (image A) are the mirror image of each other along the y-axis.

It means the pre-image of Z in quadrant 2 reflected across the y-axis to get the image in quadrant 1.

If a figure reflected across the y-axis, then rule of transformation is

`(x,y)\to (-x,y)`

So, the rule
`(x,y)\to (-x,y)` transform the pre-image of Z in quadrant 2 into its image in quadrant 1.

Therefore, the correct option is c.