Answer:
The correct option is D.
Step-by-step explanation:
From the given graph it is clear that the vertices of preimage are A(4,6), B(5,9) and C(7,6).
The vertices of image are A'(2,10), B'(3,13) and C'(5,10).
The rule of translation is defined as
[tex](x,y)\rightarrow (x+a,y+b)[/tex] .... (1)
Where, a is horizontal shift and b is vertical shift.
If a>0, then figure shifts a units right and if a<0, then figure shifts a unit left.
If b>0, then figure shifts b units up and if b<0, then figure shifts a unit down.
We have A(4,6) and A'(2,10).
[tex](4,6)\rightarrow (2,10)[/tex] .... (2)
From (1) and (2) we get
[tex]x=4,y=6[/tex]
[tex]x+a=2\Rightarrow 4+a=2\Rightarrow a=-2<0, left[/tex]
[tex]y+b=10\Rightarrow 6+b=10\Rightarrow b=4>0,up[/tex]
The rule of translation is
[tex](x,y)\rightarrow (x-2,y+4)[/tex]
The figure shifted 2 units left and 4 units up, therefore the correct option is D.
