# A line segment has endpoints at #(3 , 1)# and #(2 ,3)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #7#, and reflected about the x-axis, what will the line segment's new endpoints be?

##### 1 Answer

May 4, 2017

#### Explanation:

#"label the endpoints " A(3,1)" and " B(2,3)#

#color(blue)"First transformation "" under a rotation about O of " (3pi)/2#

#"a point " (x,y)to(y,-x)#

#rArrA(3,1)toA'(1,-3)" and " B(2,3)toB'(3,-2)#

#color(blue)"Second transformation"" under a translation " ((7),(0))#

#"a point " (x,y)to(x+7,y)" hence"#

#A'(1,-3)toA''(8,-3),B'(3,-2)toB''(10,-2)#

#color(blue)"Third transformation"" reflection in x-axis"#

#"a point " (x,y)to(x,-y)" hence"#

#A''(8,-3)toA'''(8,3),B''(10,-2)toB'''(10,2)#

#"After all 3 transformations"#

#(3,1)to(8,3)" and " (2,3)to(10,2)#