Answer:
Option C.
Step-by-step explanation:
Dilation of a line:
If center of dilation lies on the line, then the line remains same.
If center of dilation does not lies on the line, then the dilated line is parallel to the original time.
The given equation of line is
[tex]y=5x-10[/tex]
The line will remain same if center of dilation lies on this line.
For x=0,
[tex]y=5(0)-10=-10\neq 10[/tex]
It means (0,0) does not lies on given line.
For x=-5,
[tex]y=5(-5)-10=-35\neq 35[/tex]
It means (-5,35) does not lies on given line.
For x=1,
[tex]y=5(1)-10=-5[/tex]
It means (1,-5) lies on given line.
For x=2,
[tex]y=5(2)-10=0\neq 20[/tex]
It means (2,20) does not lies on given line.
Center of dilation (1,-5) could be used to support Carl's claim.
Therefore, the correct option is C.
