Question

Carl claims that for some centers of dilation of a line, the line will remain

unchanged. He is tasked to prove his claim using the line y = 5x - 10 and a dilation

with a scale factor of 2. Which center of dilation could be used to support Carl's

claim?

A. (0,0)

B. (-5, 35)

C. (1, -5)

D. (2, 20)

Answer 1

Option C.

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

`y=5x-10`

The line will remain same if center of dilation lies on this line.

For x=0,

`y=5(0)-10=-10\\eq 10`

It means (0,0) does not lies on given line.

For x=-5,

`y=5(-5)-10=-35\\eq 35`

It means (-5,35) does not lies on given line.

For x=1,

`y=5(1)-10=-5`

It means (1,-5) lies on given line.

For x=2,

`y=5(2)-10=0\\eq 20`

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.