A line segment has endpoints at (8 ,2 )(8,2) and (2 ,3 )(2,3). If the line segment is rotated about the origin by pi π, translated horizontally by - 1 −1, and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer
Jim G.
Jun 23, 2016

(8,2)to(9,-2)" and " (2,3)to(3,-3)(8,2)→(9,−2) and (2,3)→(3,−3)

Explanation:

Since there are 3 transformations to be performed on the points , name them A(8 ,2) and B(2 ,3) so we can 'track' them.

First transformation: Under a rotation about the origin of piπ

a point (x ,y) → (-x ,-y)

hence A(8 ,2) → A' (-8 ,-2) and B(2 ,3) → B'(-2 ,-3)

Second transformation: Under a translation ((-1),(0))

a point (x ,y) → (x-1 ,y)

hence A'(-8 ,-2) → A''(-9 ,-2) and B'(-2 ,-3) → B''(-3 ,-3)

Third transformation: Under a reflection in the y-axis

a point (x ,y) → (-x ,y)

hence A''(-9 ,-2) → A'''(9 ,-2) and B''(-3 ,-3) → B'''(3 ,-3)

Thus (8 ,2) → (9 ,-2) and (2 ,3) → (3 ,-3)

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