A line segment has endpoints at #(2 , 3)# and #(1 , 2)#. If the line segment is rotated about the origin by #(pi)/2 #, translated vertically by #3#, and reflected about the x-axis, what will the line segment's new endpoints be?

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Answer 1 · 2016-11-25T20:22:33

#"the line segment's new endpoints are :M(-3,1) and N (-2,2)"#

#"1- draw the points given"#

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#"2-draw a line segment from B to A"#

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#"3-rotate the line segment about origin by " pi/2#

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#"A(2,3),B(1,2) will be " A'(-3,2)" and "B' "(-2,1)" #

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#"4-now slide the segment 3 unit down"#

#"the new coordinates of A is "A''#

#A''(-3,-1)#

#"the new coordinates of B is " B''#

#B''(-2,-2)#

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#"5- now reflect the line segment by x-axis"#

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#"the reflected line segment is MN and its coordinates are :" #

#"M(-3,1) and N(-2,2)"#