Question

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

Explanation:

Step1: Analyze reflection over x - axis

A reflection over the x - axis changes the sign of the y - coordinate of a point \((x,y)\) to \((x, - y)\). By looking at the figures, we can see that the vertical orientation of the figures does not match the result of a reflection over the x - axis. So this transformation is not correct.

Step2: Analyze counterclockwise rotation of \(90^{\circ}\) about the origin

The rule for a counterclockwise rotation of \(90^{\circ}\) about the origin is \((x,y)\to(-y,x)\). When we apply this rule to the vertices of Figure A, the resulting figure does not match Figure B.

Step3: Analyze counterclockwise rotation of \(270^{\circ}\) about the origin

The rule for a counterclockwise rotation of \(270^{\circ}\) about the origin is \((x,y)\to(y, - x)\). Applying this rule to the vertices of Figure A also does not give us Figure B.

Step4: Analyze reflection over the y - axis

A reflection over the y - axis changes the sign of the x - coordinate of a point \((x,y)\) to \((-x,y)\). By visually inspecting the positions of the vertices of Figure A and Figure B, we can see that reflecting Figure A over the y - axis (changing the x - coordinates' signs) will map Figure A to Figure B.

Answer:

A reflection over the y - axis