# A line segment has endpoints at #(2 , 2)# and #(5 , 4)#. If the line segment is rotated about the origin by #(pi)/2 #, translated horizontally by #1#, and reflected about the y-axis, what will the line segment's new endpoints be?

##### 1 Answer

Jul 28, 2016

#### Explanation:

Since there are 3 transformations, name the endpoints A(2 , 2) and B(5 ,4) so we can 'track' their position after each transformation.

First transformationUnder a rotation about the origin by#pi/2# a point (x ,y) → (-y ,x)

hence A(2 ,2) → A'(-2 ,2) and B(5 ,4) → B'(-4 ,5)

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

hence A'(-2 ,2) → A''(-1 ,2) and B'(-4 ,5) → B''(-3 ,5)

Third transformationUnder a reflection in the y-axisa point (x ,y) → (-x ,y)

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

Thus

#(2,2)to(1,2)" and " (5,4)to(3,5)#