Question

what two transformations were made to triangle abc to produce triangle xyz? for these composition transformations, what are their rules? how do you know? show your work.

Explanation:

Step1: Identify the orientation change

The triangle ABC is flipped over the x - axis to change its orientation. The rule for a reflection over the x - axis is $(x,y)\to(x, - y)$. For example, point A(-5,2) becomes a point with the same x - coordinate and the opposite y - coordinate after reflection over the x - axis.

Step2: Identify the translation

After reflection, the triangle is moved 2 units to the right and 6 units down. The rule for translation is $(x,y)\to(x + 2,y-6)$. If we take a point after reflection over the x - axis and apply this translation rule, we get the corresponding point on triangle XYZ.

Answer:

The two transformations are a reflection over the x - axis with the rule $(x,y)\to(x, - y)$ and a translation 2 units to the right and 6 units down with the rule $(x,y)\to(x + 2,y - 6)$.