Question

which transformation would take figure a to figure b?

Explanation:

First, identify a key vertex of Figure A, e.g., the top-left vertex at $(-6, -1)$. The corresponding vertex on Figure B is at $(1, -1)$. Calculate the horizontal shift: $1 - (-6) = 7$, so a shift right by 7 units. Next, check the orientation: Figure A is a mirror image of Figure B across a vertical line. For a reflection over the y-axis, a point $(x,y)$ becomes $(-x,y)$. Combining these: first reflect Figure A over the y-axis (transforming $(x,y)$ to $(-x,y)$), then translate the result 7 units to the right (transforming $(-x,y)$ to $(-x + 7, y)$). Verifying with the vertex $(-6, -1)$: reflection gives $(6, -1)$, then shifting right 7 gives $(6+1, -1)=(7, -1)$? Correction: Wait, the corresponding vertex on B is $(1,-1)$. Let's use the vertex $(-1,-1)$ on A: reflection over y-axis is $(1,-1)$, which matches the top-left vertex of B. Then check the bottom vertex of A: $(-7,-9)$. Reflection over y-axis is $(7,-9)$, which matches the bottom-right vertex of B. All other corresponding vertices align with a reflection over the y-axis.

Answer:

A reflection over the y-axis (or a reflection across the line $x=0$)