Respuesta :
Option C: The line [tex]y=x[/tex] is the line of reflection.
Explanation:
It is given that the [tex]\triangle LMN[/tex] across a line, [tex]L=(12,-7)[/tex] and [tex]L'=(-7,12)[/tex]
Thus, the reflection is given by [tex](12,-7)[/tex] ⇒ [tex](-7,12)[/tex]
Now, we shall determine the line of reflection.
Option A: the x-axis
To reflect the coordinates across x-axis is given by [tex](x,y)[/tex] ⇒ [tex](x,-y)[/tex]
Thus, the line of reflection of the coordinate L across x-axis is given by
[tex](12,-7)[/tex] ⇒ [tex](12,7)[/tex]
This is not the equal to the given line of reflection [tex](12,-7)[/tex] ⇒ [tex](-7,12)[/tex]
Hence, the line of reflection is not across x-axis.
Thus, Option A is not the correct answer.
Option B : the y-axis
To reflect the coordinates across x-axis is given by [tex](x,y)[/tex] ⇒ [tex](-x,y)[/tex]
Thus, the line of reflection of the coordinate L across y-axis is given by
[tex](12,-7)[/tex] ⇒ [tex](-12,-7)[/tex]
This is not the equal to the given line of reflection [tex](12,-7)[/tex] ⇒ [tex](-7,12)[/tex]
Hence, the given line of reflection is not across y-axis.
Thus, Option B is not the correct answer.
Option C: the line [tex]y=x[/tex]
To reflect the coordinates across [tex]y=x[/tex] is given by [tex](x,y)[/tex] ⇒ [tex](y,x)[/tex]
Thus, the line of reflection of the coordinate L across the line [tex]y=x[/tex] is given by [tex](12,-7)[/tex] ⇒ [tex](-7,12)[/tex]
This is equal to the given line of reflection [tex](12,-7)[/tex] ⇒ [tex](-7,12)[/tex]
Hence, the given line of reflection is across the line [tex]y=x[/tex]
Thus, Option C is the correct answer.
Option D : the line [tex]y=-x[/tex]
To reflect the coordinates across [tex]y=-x[/tex] is given by [tex](x,y)[/tex] ⇒ [tex](-y,-x)[/tex]
Thus, the line of reflection of the coordinate L across the line [tex]y=-x[/tex] is given by [tex](12,-7)[/tex] ⇒ [tex](7,-12)[/tex]
This is not the equal to the given line of reflection [tex](12,-7)[/tex] ⇒ [tex](-7,12)[/tex]
Hence, the given line of reflection is not across the line [tex]y=-x[/tex] .
Thus, Option D is not the correct answer.
