Question

A line segment has endpoints at `(1 ,4 )` and `(3 ,9 )`. If the line segment is rotated about the origin by `pi`, translated horizontally by `- 2`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(1,4)to(-3,4)" and " (3,9)to(-5,9)`

Explanation:

Since there are 3 transformations to be performed, name the endpoints A(1 ,4) and B(3 ,9) so we can 'track' them.

First transformation Under a rotation about origin of `pi`

a point (x ,y) → (-x ,-y)

hence A(1 ,4) → A'(-1 ,-4) and B(3 ,9) → B'(-3 ,-9)

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

a point (x ,y) → (x-2 ,y)

Hence A'(-1 ,-4) → A''(-3 ,-4) and B'(-3 ,-9) → B''(-5 ,-9)

Third transformation Under a reflection in the x-axis

a point (x ,y) → (x ,-y)

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

Thus `(1,4)to(-3,4)" and " (3,9)to(-5,9)`