Question

determine a series of transformations that would map figure u onto figure v.

Explanation:

Step1: Observe orientation change

First, perform a rotation. Rotate Figure U 180 - degrees about the origin. The rule for a 180 - degree rotation about the origin for a point \((x,y)\) is \((x,y)\to(-x,-y)\).

Step2: Observe position change

Then, perform a translation. After the 180 - degree rotation, translate the figure up by a certain number of units and right by a certain number of units to match the position of Figure V. Let's assume the translation vector is \((a,b)\) where \(a\) is the horizontal displacement and \(b\) is the vertical displacement.

Answer:

A 180 - degree rotation about the origin followed by a translation.