Question

which transformation of figure a results in figure a?
a translation 3 units left and 4 units down.
a counterclockwise rotation of 90° about the origin
a reflection across the x - axis
a counterclockwise rotation of 270° about the origin

Explanation:

Step1: Recall translation rules

Translation 3 units left and 4 units down changes $(x,y)$ to $(x - 3,y - 4)$. Check if this matches.

Step2: Recall rotation rules

A counter - clockwise rotation of 90° about the origin changes $(x,y)$ to $(-y,x)$. Check if this matches.

Step3: Recall reflection rules

Reflection across the x - axis changes $(x,y)$ to $(x,-y)$. Check if this matches.

Step4: Recall rotation rules

A counter - clockwise rotation of 270° about the origin changes $(x,y)$ to $(y,-x)$. Check if this matches.
Let's assume a point $(x,y)$ on Figure A.
For a translation 3 units left and 4 units down, the new point is $(x - 3,y - 4)$.
For a counter - clockwise rotation of 90° about the origin, the new point is $(-y,x)$.
For a reflection across the x - axis, the new point is $(x,-y)$.
For a counter - clockwise rotation of 270° about the origin, the new point is $(y,-x)$.
By observing the orientation and position of Figure A and Figure A', we can see that a counter - clockwise rotation of 270° about the origin maps Figure A to Figure A'.

Answer:

a counterclockwise rotation of 270° about the origin