Question

the object was reflected across the x - axis and translated (x + 9,y - 3). the object was reflected across the x - axis and translated (x + 7,y - 5). the object was reflected across the y - axis and translated (x - 1,y - 7). the object was reflected across the y - axis and translated (x + 1,y - 7).

Explanation:

Step1: Analyze reflection across y - axis

When a point $(x,y)$ is reflected across the y - axis, the x - coordinate changes sign, becoming $(-x,y)$.

Step2: Analyze translation

The general form of a translation is $(x,y)\to(x + a,y + b)$. Given the translation $(x,y)\to(x - 1,y - 7)$.
If we start with a point $(x,y)$ on the original triangle, after reflection across the y - axis we have $(-x,y)$, and after translation we have $(-x-1,y - 7)$. This matches the transformation described in the third option.

Answer:

The object was reflected across the y - axis and translated $(x - 1,y - 7)$.