# A line segment has endpoints at #(a, b)# and #(c, d )#. The line segment is dilated by a factor of #r# around #(p,q )#. What are the new endpoints and length of the line segment?

##### 1 Answer

new length

#### Explanation:

I have a theory all these questions are here so the there's something for newbies to do. I'll do the general case here and see what happens.

We translate the plane so the dilation point P maps to the origin. Then the dilation scales the coordinates by a factor of

That's the parametric equation for a line between P and A, with

The image of

Similarly, the image of

The new length is