Question

What set of transformations could be applied to rectangle ABCD to create A'B'C'D'?

Answer 1

The correct answer is a reflection over the x-axis and then rotates counterclockwise 90 degrees.

When it is reflected over the x-axis it will be directly underneath the x-axis in the same position. It will then turn 90 degrees to the left around the origin to create the final position.

Answer 2

Vertices of the given rectangle ABCD is

A(-4,2)

B(-4,1)

C(-1,1)

D(-1,2).

Vertices of transformed rectangle A'B'C'D' are

A'(2,-4)

B'(1,-4)

C'(1,-1)

D'(2,-1)

Let us observe transformations

A(-4,2) --> A'(2,-4)

B(-4,1) --> B'(1,-4)

C(-1,1) --> C'(1,-1)

D(-1,2) --> D'(2,-1)

Form the reflected coordinates, we can clearly see that only x and y coordinates of each point are switched.

If original rectangle has vertices in form (h,k).

First if we reflect over x-axis, the coordinate(h,k) would become (h,-k).

Now if we rotate it rotated 90° counterclockwise, the x and y-coordinates switches and x-coordinate would be multiply by -1.

So, after rotated 90° counterclockwise (h,-k), we get (k,h)

So, finally the x and y-cordinates values get switched.

Therefore, correct option is third option, that is

Reflected over the x-axis and rotated 90° counterclockwise.