Question

Which sequence of transformations will change figure PQRS to figure P′Q′R′S′?

Select one:a. Counterclockwise rotation about the origin by 90 degrees followed by reflection about the x-axis

b. Counterclockwise rotation about the origin by 90 degrees followed by reflection about the y-axis
c. Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis
d. Counterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axis

Answer 1

I’m pretty sure it would be B.

Answer 2

B.

Explanation:

First, we need to compare vertices from the original figure and the transformed one.

`P(-3,-2) \implies P'(2,3)\\Q(-2,-3) \implies Q'(3, 2)\\R(-3,-4) \implies R'(4,3)\\S(-4,-4) \implies S'(4,4)`

You can observe that coordinates where changed of position. Also, the vertical coordinate of the transformed figure has opposite sign.

In other words, the transformation follows the rule

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

`P'(2,-3)\\Q'(3,-2)\\R'(4,-3)\\S'(4,-4)`

However, notice that the coordinates are not the same as the given transformation. That is because the second transformation applied was a reflection accros the x-axis which follows the rule

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

Applying the rule, we have

`P'(2,3)\\Q'(3,2)\\R'(4,3)\\S'(4,4)`

Which are congruent with the given transformed coordinates.

Therefore, the transformations are a 90° rotation counterclockwise and a reflection accros the x-axis. The right answer is B.