Question

A line segment has endpoints at `(8 ,2 )` and `(2 ,3 )`. If the line segment is rotated about the origin by `pi`, translated horizontally by `- 1`, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

`(8,2)to(9,-2)" and " (2,3)to(3,-3)`

Explanation:

Since there are 3 transformations to be performed on the points , name them A(8 ,2) and B(2 ,3) so we can 'track' them.

First transformation: Under a rotation about the origin of `pi`

a point (x ,y) → (-x ,-y)

hence A(8 ,2) → A' (-8 ,-2) and B(2 ,3) → B'(-2 ,-3)

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

a point (x ,y) → (x-1 ,y)

hence A'(-8 ,-2) → A''(-9 ,-2) and B'(-2 ,-3) → B''(-3 ,-3)

Third transformation: Under a reflection in the y-axis

a point (x ,y) → (-x ,y)

hence A''(-9 ,-2) → A'''(9 ,-2) and B''(-3 ,-3) → B'''(3 ,-3)

Thus (8 ,2) → (9 ,-2) and (2 ,3) → (3 ,-3)