Question

Consider the line y = x . If the line is dilated by a factor of 1 3 , what is the equation of the resulting line? If the resulting line is translated 1 unit down, what is the equation of the resulting line?

Please help! I'll give ten points.

Answer 1

The resulting equation after dilation: y=x.

The resulting equation after translation: y=x-1.

Explanation:

The given equation of line

`y=x`

If a line passes through the center of dilation and dilated by factor k, then the equation of line is remains same.

It is given that the line is dilated by a factor of 1/3. The center of dilation is not given so the center of dilation is (0,0).

At x=0,

`y=0`

It means the line passes through the point (0,0). Since the line passes through the center of dilation, therefore the equation of line is remains same.

`y=x`

The translation is defined as

`y=x+b`

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The resulting line is translated 1 unit down.

`y=x-1`

Therefore, the equation of the resulting line is y=x-1.