Question

which transformation would take figure a to figure b?
answer
a clockwise rotation of 270° about the origin
a reflection over the y - axis
a clockwise rotation of 90° about the origin
a reflection over the x - 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 \((x, - y)\). Let's take a vertex of Figure A, say if a vertex has coordinates \((x,y)\) in A, after reflection over x - axis it becomes \((x, - y)\). Looking at the figures, Figure B is above the x - axis and Figure A is below the x - axis. For example, if we take a point in A with y - coordinate negative, after reflection over x - axis, its y - coordinate becomes positive, which matches the position of Figure B relative to Figure A.

Step2: Analyze other options

• For a reflection over the y - axis, the x - coordinate sign changes. But the horizontal position of A and B relative to y - axis doesn't suggest a y - axis reflection.
• A clockwise rotation of \(90^{\circ}\) about the origin transforms \((x,y)\) to \((y, - x)\), which doesn't match the vertical flip - like transformation between A and B.
• A clockwise rotation of \(270^{\circ}\) about the origin transforms \((x,y)\) to \((-y,x)\), which also doesn't match the transformation between A and B.

Answer:

A reflection over the x - axis