Answer:
The rule of translation : [tex](x,y)\rightarrow (x+7,y-4)[/tex]
The vertices of image is R'(2,-9), S'(1,-9), T'(6,-3) and U'(2,-3).
Step-by-step explanation:
The vertices of a rectangle are R(-5,-5), S(-6,-5), T(-1,1), U(-5,1).
It is given that a translation maps R to the point (2,-9).
Difference between x-coordinates:
[tex]-5-2=-7[/tex]
Difference between y-coordinates:
[tex]-5-(-9)=-5+9=4[/tex]
The x-coordinate increased by 7 and y-coordinate decreased by 4. It means the figure shifts 7 units right and 4 units down.
The rule of translation is
[tex](x,y)\rightarrow (x+7,y-4)[/tex]
The vertices of image are
[tex]R(-5,-5)\rightarrow R'(-5+7,-5-4)=R'(2,-9)[/tex]
[tex]S(-6,-5)\rightarrow S'(-6+7,-5-4)=S'(1,-9)[/tex]
[tex]T(-1,1)\rightarrow T'(-1+7,1-4)=T'(6,-3)[/tex]
[tex]U(-5,1)\rightarrow U'(-5+7,1-4)=U'(2,-3)[/tex]
Therefore, the vertices of image are R'(2,-9), S'(1,-9), T'(6,-3) and U'(2,-3).
