Question

if a translation of (t_{2,-7}(x,y)) is applied to (\triangle abc), what are the coordinates of (b)? (1, -5) (-4, -10) (-3, -12) (3, -12)

Explanation:

Step1: Identify original coordinates of B

From the graph, the coordinates of point B are (- 1,-5).

Step2: Apply the translation rule

The translation rule is $T_{2,-7}(x,y)=(x + 2,y-7)$. For point B with $x=-1$ and $y = - 5$, we substitute into the rule. The new x - coordinate is $x'=-1 + 2=1$, and the new y - coordinate is $y'=-5-7=-12$.

Answer:

$(1,-12)$ (Note: There seems to be an error in the provided options as the correct answer based on the steps above is not among them. But following the steps, the correct coordinates after translation should be $(1,-12)$)