Respuesta :
Option C: [tex](6,-2)[/tex] is the image of [tex](3,2)[/tex]
Explanation:
It is given that the image of [tex](-2,5)[/tex] is [tex](1,1)[/tex]
Now, we need to find the image of [tex](3,2)[/tex] under the same translation.
First, let us determine the translation rule.
The translation rule is given by
[tex](x,y)\implies(x+h,y+k)[/tex]
Thus, we have,
[tex](-2,5)\implies(-2+h,5+k)\implies(1,1)[/tex]
Equating the corresponding x and y coordinates, we get,
x - coordinate : [tex]-2+h=1[/tex]
[tex]h=1+2[/tex]
[tex]h=3[/tex]
y - coordinate : [tex]5+k=1[/tex]
[tex]k=1-5[/tex]
[tex]k=-4[/tex]
Thus, the translation rule is given by [tex](x,y)\implies(x+3,y-4)[/tex]
Now, we shall find the image of [tex](3,2)[/tex]
Substituting the coordinate [tex](3,2)[/tex] in the translation rule [tex](x,y)\implies(x+3,y-4)[/tex], we get,
[tex](3,2)\implies(3+3,2-4)[/tex]
[tex](3,2)\implies(6,-2)[/tex]
Thus, the image of [tex](3,2)[/tex] is [tex](6,-2)[/tex]
Therefore, Option C is the correct answer.
