Question

figure x is the result of a transformation on figure w. which transformation would accomplish this?
answer
a reflection over the x -axis
a reflection over the y -axis
a rotation 90° clockwise about the origin
a rotation 90° counterclockwise about the origin

Explanation:

Step1: Analyze reflection over y - axis

A reflection over the \( y \) - axis changes the sign of the \( x \) - coordinate of a point \((x,y)\) to \((-x,y)\). Let's take a vertex of Figure \( W \), say \((-4, - 1)\) (assuming one of the vertices, we can check coordinates from the graph). After reflection over \( y \) - axis, it becomes \((4,-1)\), which matches the corresponding vertex in Figure \( X \). Let's check another vertex. If a vertex of \( W \) is \((-5,-2)\), after reflection over \( y \) - axis, it is \((5,-2)\), which also matches Figure \( X \).

Step2: Analyze other options

• Reflection over \( x \) - axis: Changes \((x,y)\) to \((x, - y)\). For a vertex \((-4,-1)\), it would become \((-4,1)\), which does not match Figure \( X \).
• Rotation \( 90^{\circ}\) clockwise about origin: The rule is \((x,y)\to(y, - x)\). For \((-4,-1)\), it becomes \((-1,4)\), not matching \( X \).
• Rotation \( 90^{\circ}\) counter - clockwise about origin: The rule is \((x,y)\to(-y,x)\). For \((-4,-1)\), it becomes \((1,-4)\), not matching \( X \).

Answer:

A reflection over the \( y \) - axis