# A line segment has endpoints at #(5 ,8 )# and #(7 ,4)#. If the line segment is rotated about the origin by #pi #, translated horizontally by #-1 #, and reflected about the y-axis, what will the line segment's new endpoints be?

##### 1 Answer

#### Explanation:

We can create a rule for this transformation.

Assume the original endpoints of the segment can be described as

The first way in which the segment is manipulated is with a rotation of

The endpoints are then translated horizontally by *horizontally* shifted, the new rule, working off the most previous rule, is:

The final transformation is a reflection over the

This is the rule for the entire transformation. Apply it to the points

#(5,8)rarr(6,-8)#

#(7,4)rarr(8,-4)#