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: Find the original coordinates of point B

From the graph, the coordinates of point B are \((1,-6)\).

Step2: Apply the translation rule \(T_{2,-6}(x,y)=(x + 2,y-6)\)

For \(x = 1\) and \(y=-6\), substitute into the rule:
\(x'=1 + 2=3\)
\(y'=-6-6=-12\)

Answer:

\((3,-12)\) (the fourth option)