A line segment has endpoints at (7 ,2 )(7,2) and (2 ,3 )(2,3). If the line segment is rotated about the origin by pi π, translated horizontally by - 4 −4, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Aug 25, 2016
Explanation:
Since there are 3 transformations to be performed here, name the endpoints A(7 ,2) and B(2 ,3) so that we can 'track' the coordinates after each transformation.
First transformation Under a rotation about the origin of
piπ a point (x ,y) → (-x ,-y)
hence A(7 ,2) → A'(-7 ,-2) and B(2 ,3) → B'(-2 ,-3)
Second transformation Under a translation
((-4),(0)) a point (x ,y) → (x-4 ,y)
hence A'(-7 ,-2) → A''(-11 ,-2) and B'(-2 ,-3) → B''(-6 ,-3)
Third transformation Under a reflection in the y-axis
a point (x ,y) → (-x ,y)
hence A''(-11 ,-2) → A'''(11 ,-2) and B''(-6 ,-3) → B'''(6 ,-3)
Thus after all 3 transformations.
(7,2)to(11,-2)" and " (2,3)to(6,-3)
