Question

A line segment has endpoints at `(7 ,4 )` and `(3 ,5 )`. If the line segment is rotated about the origin by `(3 pi)/2`, translated vertically by `-2`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

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

Explanation:

Since there are 3 transformations to be performed, name the endpoints A(7 ,4) and B(3 ,5) so that we can 'track' the coordinates of the endpoints after each transformation.

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

a point (x ,y) → (y ,-x)

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

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

a point (x ,y) → (x ,y-2)

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

Third transformation Under a reflection in the y-axis

a point (x ,y) → (-x ,y)

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

Thus after all 3 transformations the endpoints are.

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