# A line segment has endpoints at #(2 ,7 )# and #(5 ,4 )#. The line segment is dilated by a factor of #2 # around #(1 ,1 )#. What are the new endpoints and length of the line segment?

##### 1 Answer

Mar 20, 2018

(3, 13) and (9, 7);

#### Explanation:

Dilating around a point is difficult, so let's dilate around the origin. We can do this by shifting the points down by (1,1), so there are endpoints now of (1, 6) and (4, 3).

Dilating each of these is simple now: multiply the numbers by 2!

This leaves points (2, 12) and (8, 6).

We now have to shift back to the original points by adding (1,1). This means the endpoints end up at (3, 13) and (9, 7).

The length of the segment can be found with Pythagorean theorem: