Question

A line segment has endpoints at `(3 ,7 )` and `(4 ,9)`. 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

`(3,7)to(7,5) , (4,9)to(9,6)`

Explanation:

Since there are 3 transformations to be performed, name the endpoints A(3 ,7) and B(4 ,9) so that we can follow the changes that occur to them.

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

a point (x ,y) → (-y ,x)

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

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

a point (x ,y) → (x+0 ,y+2) → (x ,y+2)

hence A'(-7 ,3) → A''(-7 ,5) and B'(-9 ,4) → B''(-9 ,6)

Third transformation Under a reflection in the y-axis

a point (x ,y) → (-x ,y)

hence A''(-7 ,5) → A'''(7 ,5) and B''(-9 ,6) → B'''(9 ,6)

Thus after all 3 transformations.

`(3,7)to(7,5)" and " (4,9)to(9,6)`