Question

A line segment has endpoints at `(2 ,3 )` and `(6 ,5)`. If the line segment is rotated about the origin by `(3pi )/2`, translated horizontally by `-1`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(2.3)to(2,2) , (6,5)to(4,6)`

Explanation:

Since there are 3 transformations to be performed here, name the endpoints A(2 ,3) and B(6 ,5), so that we can follow the changes that occur.

First transformation Under a rotation about the origin of `(3pi)/2`

a point (x ,y) → (y ,-x)

hence A(2 ,3) → A'(3 ,-2) and B(6 ,5) → B'(5 ,-6)

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

a point (x ,y) → (x-1 ,y+0) → (x-1 ,y)

hence A'(3 ,-2) → A''(2 ,-2) and B'(5 ,-6) → B''(4 ,-6)

Third transformation Under a reflection in the x-axis

a point (x ,y) → (x ,-y)

hence A''(2 ,-2) → A'''(2 ,2) and B''(4 ,-6) → B'''(4 ,6)

Thus after all 3 transformations.

`(2,3)to(2,2)" and " (6,5)to(4,6)`