Question

triangle jkl is transformed by performing a 90° clockwise rotation about the origin and then a reflection over the y - axis, creating triangle jkl. which transformation will map jkl back to jkl?
a reflection over the x - axis and then a reflection over the y - axis
a reflection over the y - axis and then a 90° clockwise rotation about the origin
a reflection over the x - axis and then a 90° clockwise rotation about the origin
a reflection over the x - axis and then a 90° counterclockwise rotation about the origin

Explanation:

Step1: Analyze the original transformations

Let's assume a point \((x,y)\) in triangle \(JKL\).

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

Step2: Analyze the reverse transformations

We want to map \((-y,-x)\) back to \((x,y)\)

• First, a reflection over the \(x\) - axis: \((-y,-x)\to(-y,x)\)
• Then a \(90^{\circ}\) clockwise rotation about the origin: \((-y,x)\to(x,y)\)

Answer:

a reflection over the \(x\) - axis and then a \(90^{\circ}\) clockwise rotation about the origin