Question

which transformation would take figure a to figure b? answer a counterclockwise rotation of 90° about the origin a counterclockwise rotation of 270° about the origin a reflection over the y - axis a reflection over the x - axis

Explanation:

First, identify a key vertex of Figure A, for example, the vertex at (9,1). Test each transformation:

1. Counterclockwise 90° rotation about origin: The rule is $(x,y) \to (-y,x)$. Applying this to (9,1) gives $(-1,9)$, which does not match a vertex of Figure B.
2. Counterclockwise 270° rotation about origin: The rule is $(x,y) \to (y,-x)$. Applying this to (9,1) gives $(1,-9)$, which does not match a vertex of Figure B.
3. Reflection over the y-axis: The rule is $(x,y) \to (-x,y)$. Applying this to (9,1) gives $(-9,1)$, which is a vertex of Figure B. Testing another vertex of A, like (3,2), reflection over y-axis gives $(-3,2)$, which is also a vertex of Figure B.
4. Reflection over the x-axis: The rule is $(x,y) \to (x,-y)$. Applying this to (9,1) gives $(9,-1)$, which does not match a vertex of Figure B.

All matching vertices confirm the correct transformation.

Answer:

A reflection over the y-axis