# A line segment has endpoints at #(9 ,6 )# and #(5 ,3)#. If the line segment is rotated about the origin by #pi /2 #, translated vertically by #2 #, and reflected about the x-axis, what will the line segment's new endpoints be?

##### 1 Answer

Nov 10, 2016

#### Explanation:

Since there are 3 transformations to be performed here, label the points A(9 ,6) and B(5 ,3) so that the change to each point after each transformation can be noted.

First transformationUnder a rotation about the origin if#pi/2#

#" a point" (x,y)to(y,-x)# hence A(9 ,6) →A'(6 ,-9) and B(5 ,3) → B'(3 ,-5)

Second transformationUnder a translation#((0),(2))#

#" a point" (x,y)to(x+0,y+2)# hence A'(6 ,-9) → A''(6 ,-7) and B'(3 ,-5) → B''(3 ,-3)

Third transformationUnder a reflection in the x-axis

#" a point" (x,y)to(x,-y)# hence A''(6 ,-7) → A'''(6 ,7) and B''(3 ,-3) → B'''(3 ,3)

After all 3 transformations.

#(9,6)to(6,7)" and " (5,3)to(3,3)#