A line segment has endpoints at #(7 ,6 )# and #(5 ,3 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 4 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Feb 9, 2017
Explanation:
Since there are 3 transformations to be performed here, label the endpoints A(7 ,6) and B(5 ,3)
#color(blue)"First transformation"- "Under a rotation about origin of "pi#
#"a point "(x,y)to(-x,-y)# Hence A(7 ,6) → A'(-7 ,-6) and B(5 ,3) → B'(-5 ,-3)
#color(blue)"Second transformation "-"Under a translation" ((-4),(0))#
#"a point "(x,y)to(x-4,y)# Hence A'(-7 ,-6) → A''(-11 ,-6) and B'(-5 ,-3) →B''(-9 ,-3)
#color(blue)"Third transformation"-" Under a reflection in the y-axis"#
#"a point "(x,y)to(-x,y)# Hence A''(-11 ,-6) → A'''(11 ,-6) and B''(-9 ,-3) → B'''(9 ,-3)
After all 3 transformations.
#(7,6)to(11,-6)" and " (5,3)to(9,-3)#
