# A line segment has endpoints at #(1 ,6 )# and #(5 ,1 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 4 #, and reflected about the y-axis, what will the line segment's new endpoints be?

##### 1 Answer

Nov 24, 2017

See explanation.

#### Explanation:

The starting points' coordinates are:

#A=(1,6)#

and

#B=(5,1)#

**I step** - rotate about origin.

Rotating about origin by **both** coordinates to opposite numbers, so the new coordinates are:

#A_1=(-1,-6)#

and

#B_1=(-5,-1)#

**II step** - translation

Translating horizontally by

#A_2=(-5,-6)#

and

#B_2=(-9,-1)#

**II step** - reflect about

Reflecting about

#A_3=(5,-6)#

and

#B_3=(9,-1)#

Finally we can say that the new coordinates are: