Question

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

Explanation:

Step1: Recall reflection and rotation rules

• Reflection over \(x -\)axis: \((x,y)\to(x, - y)\)
• Reflection over \(y -\)axis: \((x,y)\to(-x,y)\)
• Counter - clockwise rotation of \(90^{\circ}\) about the origin: \((x,y)\to(-y,x)\)
• Counter - clockwise rotation of \(270^{\circ}\) about the origin: \((x,y)\to(y, - x)\)

Step2: Analyze the transformation

If we consider a general point \((x,y)\) on Figure A. After a reflection over the \(x -\)axis, the \(y -\)coordinate changes its sign. Looking at the positions of Figure A and Figure B, if we take a point \((x,y)\) on Figure A, the corresponding point on Figure B is \((x,-y)\) (for example, if we assume a vertex of Figure A has coordinates \((3,-4)\), the corresponding vertex of Figure B has coordinates \((3,4)\))

Answer:

A reflection over the \(x -\)axis