A line segment has endpoints at #(3 ,7 )# and #(4 ,9)#. If the line segment is rotated about the origin by #(pi )/2 #, translated vertically by #2 #, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

#(3,7)to(7,5) , (4,9)to(9,6)#

Since there are 3 transformations to be performed, name the endpoints A(3 ,7) and B(4 ,9) so that we can follow the changes that occur to them.

First transformation Under a rotation about the origin of #pi/2#

a point (x ,y) → (-y ,x)

hence A(3 ,7) → A'(-7 ,3) and B(4 ,9) → B'(-9 ,4)

Second transformation Under a translation #((0),(2))#

a point (x ,y) → (x+0 ,y+2) → (x ,y+2)

hence A'(-7 ,3) → A''(-7 ,5) and B'(-9 ,4) → B''(-9 ,6)

Third transformation Under a reflection in the y-axis

a point (x ,y) → (-x ,y)

hence A''(-7 ,5) → A'''(7 ,5) and B''(-9 ,6) → B'''(9 ,6)

Thus after all 3 transformations.

#(3,7)to(7,5)" and " (4,9)to(9,6)#

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Answer 2

Sadie Allen

The new endpoints of the line segment after the given transformations will be (-7, 4) and (-9, 3).

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Answer from HIX Tutor

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