Question

answer
a reflection over the x - axis
a rotation 90° clockwise about the
origin
a reflection over the y - axis
a rotation 90° counterclockwise
about the origin

Explanation:

Step1: Recall reflection and rotation properties

Reflection over \(y -\)axis: \((x,y)\to(-x,y)\). Rotation \(90^{\circ}\) clockwise: \((x,y)\to(y, - x)\). Rotation \(90^{\circ}\) counter - clockwise: \((x,y)\to(-y,x)\). Reflection over \(x -\)axis: \((x,y)\to(x,-y)\).

Step2: Analyze the transformation of Figure \(X\) to Figure \(Y\)

Let's assume a point \((x,y)\) on Figure \(X\). For Figure \(Y\), if we consider the symmetry about the \(y -\)axis. For example, if a point on Figure \(X\) is \((- 3,1)\), the corresponding point on Figure \(Y\) is \((3,1)\). Using the rule \((x,y)\to(-x,y)\) (reflection over \(y -\)axis).

Answer:

A reflection over the \(y -\)axis.