A line segment has endpoints at #(6 ,5 )# and #(8 ,7 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # 2 #, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
#color(violet)("After all 3 transformations " color(green)((7, 4)to(-4, -5)" and "(-7, -8)to(-7, 8)#
Explanation:
#"since there are 3 transformations to be performed"#
#"label the endpoints"#
#A(6,5)" and "B(8,7)#
#color(maroon)"transformation of rotation about the origin of "pi#
#rArrA(6, 5)toA'(-6, -5)#
#rArrB(8, 7)toB'(-7, -8)#
#color(maroon)"next transformation under a horizontal translation "((2),(0))#
#• " a point "(x,y)to(x + 2, y)#
#rArrA'(-6, -5) to A''(-4, -5)#
#rArrB'(-7, -8) to B''(-5, -8)#
#color(maroon)"last transformation under a reflection in the x-axis"#
#• " a point "(x,y)to(x,-y)#
#rArrA''(-4, -5)toA'''(-4, 5)#
#rArrB''(-7, -8)toB'''(-7, 8)#
#color(violet)("After all 3 transformations " color(green)((7, 4)to(-4, -5)" and "(-7, -8)to(-7, 8)#
