A line segment has endpoints at #(2 ,5 )# and #(7 , 3 )#. 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
Jim G.
Jul 12, 2017

#4,2)" and " (2,7)#

Explanation:

Since there are 3 transformations to be performed label the endpoints A(2,5) and B(7,3)

#color(blue)"First transformation"#

#"under a rotation about the origin of "pi/2#

#• " a point "(x,y)to(-y,x)#

#rArrA(2,5)toA'(-5,2),B(7,3)toB'(-3,7)#

#color(blue)"Second transformation"#

#"under a translation "((1),(0))#

#• " a point "(x,y)to(x+1,y)#

#rArrA'(-5,2)toA''(-4,2)#

#rArrB'(-3,7)toB''(-2,7)#

#color(blue)"Third transformation"#

#"under a reflection in the y-axis"#

#• " a point "(x,y)to(-x,y)#

#rArrA''(-4,2)toA'''(4,2),B#

#rArrB''(-2,7)toB'''(2,7)#

#"hence after all 3 transformations"#

#(2,5)to(4,2)" and " (7,3)to(2,7)#

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