# A line segment has endpoints at #(7 ,4 )# and #(3 ,5 )#. If the line segment is rotated about the origin by #(3 pi)/2 #, translated vertically by #-2 #, and reflected about the y-axis, what will the line segment's new endpoints be?

##### 1 Answer

Aug 24, 2016

#### Explanation:

Since there are 3 transformations to be performed, name the endpoints A(7 ,4) and B(3 ,5) so that we can 'track' the coordinates of the endpoints after each transformation.

First transformationUnder a rotation about the origin of#(3pi)/2# a point (x ,y) → (y ,-x)

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

Second transformationUnder a translation of#((0),(-2))# a point (x ,y) → (x ,y-2)

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

Third transformationUnder a reflection in the y-axisa point (x ,y) → (-x ,y)

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

Thus after all 3 transformations the endpoints are.

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