Question

if a translation of t_{2, -7}(x, y) is applied to △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 $T_{2,-7}(x,y)=(x + 2,y-7)$. Substitute $x=-1$ and $y = - 5$ into the rule. For the x - coordinate of B', we have $x'=-1 + 2=1$. For the y - coordinate of B', we have $y'=-5-7=-12$. So the coordinates of B' are $(1,-12)$. But there is an error above. Let's correct it.
From the graph, the coordinates of point B are $(1,-5)$.
Apply the translation rule $T_{2,-7}(x,y)=(x + 2,y-7)$.
For the x - coordinate of B': $x=1$, then $x'=1 + 2=3$.
For the y - coordinate of B': $y=-5$, then $y'=-5-7=-12$.

Answer:

(3,-12)