Question

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

Explanation:

Step1: Recall rotation rules

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

Step2: Analyze the transformation

Let's assume a point \((x,y)\) on Figure A. If we rotate a point \((x,y)\) counter - clockwise \(270^{\circ}\) about the origin, using the rule \((x,y)\to(y, - x)\).
If we consider the orientation and position of the figures, a counter - clockwise rotation of \(270^{\circ}\) about the origin will map Figure A to Figure B.

Answer:

A counterclockwise rotation of \(270^{\circ}\) about the origin.