A line segment has endpoints at #(1 ,2 )# and #(9 ,3 )#. If the line segment is rotated about the origin by #( 3 pi)/2 #, translated horizontally by # 2 #, and reflected about the x-axis, what will the line segment's new endpoints be?
2 Answers
#color(brown)("After all 3 transformations " color(orange)((1, 2)to(4, 1)" and "(9, 3)to(5, 9)#
Explanation:
#"since there are 3 transformations to be performed"#
#"label the endpoints"#
#A(1, 2)" and "B(9, 3)#
#color(indigo)"transformation of rotation about the origin of "(3pi) / 2#
#rArrA(1, 2)toA'(2, -1)#
#rArrB(9, 3)toB'(3, -9)#
#color(indigo)"next transformation under a horizontal translation " ((2),(0))#
#• " a point "(x,y)to(x + 2, y)#
#rArrA'(2, -1) to A''(4, -1)#
#rArrB'(3, -9) to B''(5, -9)#
#color(indigo)"last transformation under a reflection in the x -axis"#
#• " a point "(x,y)to(x, -y)#
#rArrA''(4, -1)toA'''(4, 1)#
#rArrB''(5, -9)toB'''(5, 9)#
#color(brown)("After all 3 transformations " color(orange)((1, 2)to(4, 1)" and "(9, 3)to(5, 9)#
Explanation:
#"Since there are 3 transformations to be performed label"#
#"the endpoints"#
#A=(1,2)" and "B=(9,3)#
#color(blue)"first transformation"#
#"under a rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#A(1,2)toA'(2,-1)#
#B(9,3)toB'(3,-9)#
#color(blue)"second transformation"#
#"under a horizontal translation "((2),(0))#
#• " a point "(x,y)to(x+2,y)#
#A'(2,-1)toA''(4,-1)#
#B'(3,-9)toB''(5,-9)#
#color(blue)"third transformation"#
#"under a reflection in the x-axis"#
#• " a point "(x,y)to(x,-y)#
#A''(4,-1)toA'''(4,1)#
#B''(5,-9)toB'''(5,9)#
#"After all 3 transformations"#
#(1,2)to(4,1)" and "(9,3)to(5,9)#
