# A line segment goes from #(4 ,1 )# to #(2 ,3 )#. The line segment is dilated about #(2 ,2 )# by a factor of #2#. Then the line segment is reflected across the lines #x = -2# and #y=4#, in that order. How far are the new endpoints form the origin?

##### 1 Answer

I get

#### Explanation:

Yikes, that's a lot of transformations. We're just interested in the image of each endpoint.

To do the dilation we start by getting a direction vector from the dilation point to each endpoint, essentially translating the dilation point to the origin.

We dilate each direction vector by a factor of two and translate back:

Reflecting through

Reflecting through

If I did that right the first endpoint is *is* the origin, so a distance of zero.