Question

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

Explanation:

Step1: Analyze reflection over y - axis

A reflection over the \(y\) - axis changes the \(x\) - coordinate of a point \((x,y)\) to \((-x,y)\). Let's take a vertex of Figure A, say, if we consider a point \((-8,4)\) on Figure A. After reflection over the \(y\) - axis, it would become \((8,4)\). Looking at Figure B, we can see that the corresponding points seem to have this relationship. Let's check another point. A point \((-2,5)\) on Figure A, after reflection over \(y\) - axis, becomes \((2,5)\), which matches the position of a point on Figure B.

Step2: Analyze reflection over x - axis

A reflection over the \(x\) - axis changes the \(y\) - coordinate of a point \((x,y)\) to \((x, - y)\). If we take the point \((-8,4)\) on Figure A, after reflection over \(x\) - axis, it would be \((-8,-4)\), which is not in the position of Figure B, so this is not the transformation.

Step3: Analyze \(90^{\circ}\) clockwise rotation

A \(90^{\circ}\) clockwise rotation about the origin transforms a point \((x,y)\) to \((y,-x)\). For the point \((-8,4)\), after \(90^{\circ}\) clockwise rotation, it becomes \((4,8)\), which is not in the position of Figure B.

Step4: Analyze \(270^{\circ}\) clockwise rotation

A \(270^{\circ}\) clockwise rotation about the origin is equivalent to a \(90^{\circ}\) counter - clockwise rotation, and it transforms a point \((x,y)\) to \((-y,x)\). For the point \((-8,4)\), after \(270^{\circ}\) clockwise rotation, it becomes \((-4,-8)\), which is not in the position of Figure B.

Answer:

A reflection over the y - axis