Question

determine a series of transformations that would map figure s onto figure t.

answer
a rotation of 180° clockwise about the origin
followed by a translation unit(s).

Explanation:

Step1: Analyze the rotation

First, we know that a \(180^{\circ}\) clockwise rotation about the origin \((x,y)\to(-x, -y)\). After rotation, we need to check the translation.

Step2: Analyze the translation

Let's assume a general point \((x,y)\) on Figure \(S\). After \(180^{\circ}\) clockwise rotation about the origin, it becomes \((-x,-y)\). By comparing the positions of corresponding points of the rotated - Figure \(S\) (after \(180^{\circ}\) rotation) and Figure \(T\), we find that we need to move the rotated figure \(4\) units down.

Answer:

A rotation of \(180^{\circ}\) clockwise about the origin followed by a translation \(4\) units down.