Question

which transformation would take figure a to figure b? (graph of coordinate plane with figure a and figure b, then answer options: 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 should be \((x, - y)\). Looking at the figures, Figure B is above the x - axis and Figure A is below. Let's check a key point. For example, the bottom - most point of A (let's assume its coordinates are around \((3,-9)\)) after reflection over x - axis would be \((3,9)\), which matches the top - most region of B.

Step2: Analyze other options

• Reflection over y - axis: A reflection over y - axis changes \((x,y)\) to \((-x,y)\). The figures are not mirror images over the y - axis as the left - right orientation doesn't match this transformation.
• Clockwise rotation of \(90^{\circ}\) about origin: A clockwise rotation of \(90^{\circ}\) about the origin transforms \((x,y)\) to \((y, - x)\). This would change the shape's orientation in a way that doesn't match the transformation from A to B.
• Clockwise rotation of \(270^{\circ}\) about origin: A clockwise rotation of \(270^{\circ}\) about the origin is equivalent to a counter - clockwise rotation of \(90^{\circ}\), transforming \((x,y)\) to \((-y,x)\), which also doesn't match the transformation from A to B.

Answer:

A reflection over the x - axis