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 \((1,-5)\).

Step2: Apply the translation rule \(T_{2,-7}(x,y)=(x + 2,y-7)\)

For \(x = 1\), \(x+2=1 + 2=3\).
For \(y=-5\), \(y - 7=-5-7=-12\).
So the coordinates of \(B'\) are \((3,-12)\).

Answer:

D. (3, -12)