# A line segment has endpoints at #(8 ,5 )# and #(2 ,1 )#. 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

Jun 2, 2016

(8 ,5) → (9 ,-5) and (2 ,1) → (3 ,-1)

#### Explanation:

I am naming the endpoints A (8 ,5) and B (2 ,1) so we can follow what happens to each after each of the 3 transformations.

First transformationrotation about origin of#pi# a point (x ,y) → (-x ,-y)

hence A (8 ,5) → A' (-8 ,-5) and B (2 ,1) → B'(-2 ,-1)

Second transformationUnder a translation of#((-1),(0))# a point (x ,y) → (x-1 ,y)

hence A' (-8 ,-5) → A''(-9 ,-5) and B' (-2 ,-1) →B'' (-3 ,-1)

Third transformationReflection in the y-axisa point (x ,y) → (-x ,y)

hence A'' (-9 ,-5) → (A''' (9 ,-5) and B'' (-3 ,-1) → B''' (3 ,-1)

Thus (8 ,5) → (9 ,-5) and (2 ,1) → (3 ,-1)