Question

which pair of transformations is the same as a reflection across the y - axis?
a a rotation of 90° counter - clockwise and a reflection across the x - axis
b a rotation of 90° clockwise and a reflection across the y - axis
c a rotation of 180° and a reflection across the x - axis
d a rotation of 180° and a reflection across the y - axis

Explanation:

Step1: Recall transformation rules

Let a point be \((x,y)\). A reflection across the \(y -\)axis changes it to \((-x,y)\).

Step2: Analyze option C

For a point \((x,y)\), a rotation of \(180^{\circ}\) about the origin changes it to \((-x,-y)\). Then a reflection across the \(x - \)axis changes \((-x,-y)\) to \((-x,y)\) which is the same as a reflection across the \(y - \)axis.

Answer:

C. a rotation of \(180^{\circ}\) and a reflection across the \(x - \)axis