Question

identify the transformation. translation 5 units right, 1 unit down translation 5 units left, 1 unit up. 90 rotation counter clockwise reflection across y - axis

Explanation:

Step1: Analyze translation

Translation moves the figure without rotation or reflection. The figure here is not just moved (translation would keep orientation same in terms of left - right/up - down relative positions, but here orientation changes).

Step2: Analyze rotation

Rotation changes the orientation of the figure. A \(90^{\circ}\) counter - clockwise rotation would change the relative positions of points in a circular - motion - like way. But looking at the symmetry of the figure across the \(y\) - axis (if we consider a point \((x,y)\) on one figure, the corresponding point on the other figure is \((-x,y)\))

Step3: Analyze reflection

Reflection across the \(y\) - axis transforms a point \((x,y)\) to \((-x,y)\). If we assume a general point on one of the curved - shape figures (say a point on the right - hand side figure with \(x>0\)), its image on the left - hand side figure has \(x\) coordinate negated (while \(y\) remains the same in terms of vertical position relative to the axis), which is the property of reflection across the \(y\) - axis.

Answer:

Reflection across \(y\) - axis