Question

describe a sequence of transformations that will map xyz on abc

Explanation:

Step1: Analyze orientation change

A 180 - degree counter - clockwise rotation about the origin changes the orientation of the triangle $\triangle XYZ$ to match the general orientation of $\triangle A'B'C'$ (here represented as $\triangle X'Y'Z'$). The rule for a 180 - degree counter - clockwise rotation about the origin $(0,0)$ for a point $(x,y)$ is $(x,y)\to(-x,-y)$.

Step2: Analyze position adjustment

After the rotation, a translation is needed to map the triangle exactly. By observing the x - coordinates of corresponding points, we can see that a translation 1 unit to the right is required. The rule for a translation 1 unit to the right for a point $(x,y)$ is $(x,y)\to(x + 1,y)$.

Answer:

First, rotate $\triangle XYZ$ 180 degrees counter - clockwise about the origin, then translate the resulting triangle 1 unit to the right.