Question

A line segment has endpoints at `(2 , 2)` and `(5 , 4)`. If the line segment is rotated about the origin by `(pi)/2`, translated horizontally by `1`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

`(2,2)to(1,2)" and " (5,4)to(3,5)`

Explanation:

Since there are 3 transformations, name the endpoints A(2 , 2) and B(5 ,4) so we can 'track' their position after each transformation.

First transformation Under a rotation about the origin by `pi/2`

a point (x ,y) → (-y ,x)

hence A(2 ,2) → A'(-2 ,2) and B(5 ,4) → B'(-4 ,5)

Second transformation Under a translation `((1),(0))`

a point (x ,y) → (x+1 ,y)

hence A'(-2 ,2) → A''(-1 ,2) and B'(-4 ,5) → B''(-3 ,5)

Third transformation Under a reflection in the y-axis

a point (x ,y) → (-x ,y)

hence A''(-1 ,2) → A'''(1 ,2) and B''(-3 ,5) → B'''(3 ,5)

Thus `(2,2)to(1,2)" and " (5,4)to(3,5)`