Question

which set of transformations will map figure stuvw onto figure mnopq? a. a reflect - across the x - axis, and then a reflection across the y - axis b. a translation 4 units down, and then a reflection across the y - axis c. a 90 - counterclockwise rotation about the origin, and then a reflection across the y - axis d. a 90 - counterclockwise rotation about the origin, and then a reflection across the x - axis

Explanation:

Step1: Analyze option A

A reflection across the x - axis changes the sign of the y - coordinates of the points of Figure STUVW. Then a reflection across the y - axis changes the sign of the x - coordinates. This will not map Figure STUVW onto Figure MNOPQ.

Step2: Analyze option B

A translation 4 units down changes the y - coordinates of the points of Figure STUVW by subtracting 4 from each y - coordinate. Then a reflection across the y - axis changes the sign of the x - coordinates. This will not map the figure as required.

Step3: Analyze option C

A 90 - degree counter - clockwise rotation about the origin has the transformation rule \((x,y)\to(-y,x)\). Then a reflection across the y - axis (changing the sign of the x - coordinates) will map Figure STUVW onto Figure MNOPQ.

Step4: Analyze option D

A 90 - degree clockwise rotation about the origin has the transformation rule \((x,y)\to(y, - x)\). Then a reflection across the x - axis (changing the sign of the y - coordinates) will not map Figure STUVW onto Figure MNOPQ.

Answer:

C. a 90 - degree counter - clockwise rotation about the origin, and then a reflection across the y - axis