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

##### 1 Answer

Jul 30, 2016

#### Explanation:

Since there are 3 transformations to be performed, name the endpoints A(9 ,6) and B(5 ,3). This will enable us to 'track' the position of the points after each transformation.

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

hence A(9 ,6) → A'(-9 ,-6) and B(5 ,3) → B'(-5 ,-3)

Second transformationUnder a translation#((0),(2))# a point (x ,y) → (x ,y+2)

hence A'(-9 ,-6) → A''(-9 ,-4) and B'(-5 ,-3) → B''(-5 ,-1)

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

hence A''(-9 ,-4) → A'''(-9 ,4) and B''(-5 ,-1) → B'''(-5 ,1)

Thus after the 3 transformations.

#(9,6)to(-9,4)" and " (5,3)to(-5,1)#