A line segment has endpoints at #(1 ,2 )# and #(9 ,4 )#. If the line segment is rotated about the origin by #( 3 pi)/2 #, translated vertically by # 3 #, and reflected about the x-axis, what will the line segment's new endpoints be?
2 Answers
#color(chocolate)("After all 3 transformations " color(maroon)((1, 2)to(-2, -2)" and "(9, 4)to(4, 6)#
Explanation:
#"since there are 3 transformations to be performed"#
#"label the endpoints"#
#A(1, 2)" and "B(9, 4)#
#color(purple)"transformation of rotation about the origin of "(3pi) /2 #
#rArrA(1, 2)toA'(2, -1)#
#rArrB(9, 4)toB'(4, -9)#
#color(purple)"next transformation under a vertical translation " ((0),(3))#
#• " a point "(x,y)to(x, y + 3)#
#rArrA'(2, -1) to A''(2, 2)#
#rArrB'(4, -9) to B''(4, -6)#
#color(purple)"last transformation under a reflection in the x -axis"#
#• " a point "(x,y)to(x, -y)#
#rArrA''(2, 2)toA'''(-2, -2)#
#rArrB''(4, -6)toB'''(4, 6)#
#color(chocolate)("After all 3 transformations " color(maroon)((1, 2)to(-2, -2)" and "(9, 4)to(4, 6)#
Explanation:
#"Since there are 3 transformations to be performed label"#
#"the endpoints"#
#A=(1,2)" and "B=(9,4)#
#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(9,4)toB'(4,-9)#
#color(blue)"second transformation"#
#"under a vertical translation "((0),(3))#
#"a point "(x,y)to(x,y+3)#
#A'(2,-1)toA''(2,2)#
#B'(4,-9)toB''(4,-6)#
#color(blue)"third transformation"#
#"under a reflection in the x-axis"#
#"a point "(x,y)to(x,-y)#
#A(2,2)toA'''(2,-2)#
#B''(4,-6)toB'''(4,6)#
#"After all 3 transformations"#
#(1,2)to(2,-2)" and "(9,4)to(4,6)#
