# A line segment has endpoints at #(7 ,6 )# and #(2 ,3 )#. 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

Jun 1, 2016

(7 ,6) → (11 ,-6)

(2 ,3) → (6 ,-3)

#### Explanation:

There are 3 transformations here. I am naming the points A(7 ,6) and B(2 ,3) so that we can follow what happens to them after each transformation.

1st transformation: under a rotation about origin of#pi# a point (x ,y) → (-x ,-y)

hence A (7 ,6) → A'(-7 ,-6) and B(2 ,3) → B'(-2 ,-3)

2nd transformation: under a translation of#((-4),(0))# a point (x ,y) → (x-4 ,y)

hence A'(-7 ,-6) → A'' (-11 ,-6) and B'(-2 ,-3) → B''(-6 ,-3)

3rd transformation: under a reflection in the y-axisa point (x ,y) → (-x ,y)

hence A''(-11 ,6) → A'''(11 ,-6) and B''(-6 ,-3) → B'''(6 ,-3)

Thus A(7 ,6) → (11 ,-6) and B(2 ,3) → (6 ,-3)