Question

press \try\ to test a transformation or sequence of transformations.
a rotation of 90° counterclockwise about the origin followed by a translation right unit(s).

Explanation:

Step1: Analyze the rotation

When a figure is rotated \(90^{\circ}\) counter - clockwise about the origin, the transformation rule for a point \((x,y)\) is \((x,y)\to(-y,x)\).

Step2: Analyze the translation

After rotation, to get from the rotated figure to the final position (assuming we are comparing Figure U and Figure T in a standard coordinate - based transformation analysis), we count the horizontal shift. If we consider a reference point (say a vertex of the polygon), after rotation, we need to move it to the right. By observing the \(x\) - coordinates of corresponding vertices, we find that the number of units of translation to the right is \(5\).

Answer:

\(5\)