Question

A line segment has endpoints at `(5 , 2)` and `(3 , 1)`. If the line segment is rotated about the origin by `(3pi)/2`, translated vertically by `4`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

(5 ,2) → (-2 ,-1) and (3 ,1) → (-1 ,1)

Explanation:

Since there are 3 transformations to be performed here , name the endpoints A(5 ,2) and B(3 ,1) so we can follow how each point is altered after each transformation.

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

a point (x ,y) → (y ,-x)

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

Second transformation: Under a translation of `((0),(4))`

a point (x ,y) → (x ,y+4)

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

Third transformation: Under a reflection in y-axis

a point (x ,y) → (-x ,y)

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

Thus (5 ,2) → (-2 ,-1) and (3 ,1) → (-1 ,1)