Question

Which transformation can be applied to the blue figure to create the red figure?

A: Rotation 90° counterclockwise around the origin, and then reflection across the y-axis

B: Rotation 180° around the origin, and then reflection across the y-axis

C: Reflection across the x-axis, and then rotation 90° counterclockwise around the origin

D: Reflection across the line y=-x, and then rotation 270° counterclockwise around the origin

Answer 1

Answer:

D

Step-by-step explanation:

From the figure, the transformation that can be applied to the blue figure to create the red figure has the rule:

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

Now,

1. Reflection across the line y=-x has the rule

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

2. Rotation 270° counterclockwise around the origin has the rule

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

3. Reflection across the line y=-x, and then rotation 270° counterclockwise around the origin has the rule

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

As you can see, given transformation is equivalent to the sequense of transformations from option D

Answer 2

Answer:

D: Reflection across the line y=-x, and then rotation 270° counterclockwise around the origin

Step-by-step explanation:

The red figure is just a reflection of the blue figure along the y-axis

The same result can be obtained by these two transformations:

1) Reflection across the line y = -x

And then

2) Rotation 270° counterclockwise around the origin