Answer:
The correct option is D.
Step-by-step explanation:
From the given graph it is clear that the vertices of triangle ABC are A(-10,-9), B(15,-10), C(-16,5) and the vertices of triangle JKL are J(-3,-5), K(-22,-6), L(-9,9).
It is given that the graph shows a translation from preimage triangle ABC to image triangle JKL.
[tex](x,y)\rightarrow (x+a,y+b)[/tex] .... (1)
We know that image of A(-10,-9) is J(-3,5).
[tex]A(-10,-9)\rightarrow J(-3,-5)[/tex] .... (2)
From (1) and (2), we get
[tex]x=-10,y=-9,x+a=-3,y+b=-5[/tex]
[tex]x+a=-3[/tex]
[tex](-10)+a=-3[/tex]
[tex]a=-3+10=7[/tex]
[tex]y+b=5[/tex]
[tex]-9+b=-5[/tex]
[tex]b=-5+9=4[/tex]
The value of a is 7 and the value of b is 4. So the required rule for translation is
[tex](x,y)\rightarrow (x+7,y+4)[/tex]
Therefore option D is correct.
