Question

A line segment has endpoints at `(6 ,2 )` and `(5 ,7)`. 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

`(6,2)to(2,8),(5,7)to(7,7)`

Explanation:

Since there are 3 transformation to be performed, name the endpoints A(6 ,2) and B(5 ,7) so that we can 'track' the changes after each transformation.

First transformation: Under a rotation about origin of `pi/2`

a point (x ,y) → (-y ,x)

hence A(6 ,2) → A'(-2 ,6) and B(5 ,7) → B'(-7 ,5)

Second transformation: Under a translation `((0),(2))`

a point (x ,y) → (x ,y+2)

hence A'(-2 ,6) → A''(-2 ,8) and B'(-7 ,5) → B''(-7 ,7)

Third transformation: Under a reflection in the y-axis

a point (x ,y) → (-x ,y)

hence A''(-2 ,8) → A'''(2 ,8) and B''(-7 ,7) → B'''(7 ,7)

Thus `(6,2)to(2,8)" and " (5,7)to(7,7)`