A reflection in the y-axis followed by a reflection in the x-axis does not give the same result as which of the following transformations?

Question

A. A reflection in the x-axis followed by a reflection in the y-axis

 

B. A rotation of 180 degrees

 

C. A rotation of 90 degrees followed by a reflection in the x-axis

 

D. A reflection in the line y = x followed by a reflection in the line y = -x

Answer 1

Hi Hannah,

 

If you could cut a piece of graph paper into 4 pieces, draw this same thing on all four:  a rectangle with coordinates A(1,3), B(2,3), C(2,6), and D(1,6).    Also, onto each graph, draw the given reflection in the y-axis followed by the x-axis, resulting in the image rectangle at A'(-1,-3), B'(-2,-3), C'(-2,-6) and D'(-1,-6).  Do these in a one color.

 

Try out A on one of these grids:  Do the reflection in x-axis followed by the reflection in the y-axis with a different color.  Does your new image land on top of the original image?  (YES)

 

Try out B on a different of the four girds: Daw a line from the origin to the closet corner of the rectangle. Now rotate the line around the origin - the line goes from the origin to A, so after the 180 degree rotation, the original A should land right on top of the original A'.  Therefore, B works.

 

Try out C on a different grid.  The 90 degree rotation makes A''(-3,1).  Reflecting just these two points across the x-axis, A''' does not land on the original A', but instead at A'''(-3,-1)  so C does NOT work.

 

Just to be sure, take the 4th grid and draw a dashed line y=x, and a dashed line y=-x.  Trace over your original rectangle ABCD with a dark marker.  Fold the paper on the dashed line y=x, and trace the image it leaves in the second quadrant with this dark marker.   Now fold the paper on the line y=-x.  Does the newest image land on the original A'B'C'D'?  (Yes - so D works).

 

 

Final answer:  only C does not work.