Question

A line segment has endpoints at `(9 ,6 )` and `(5 ,3)`. If the line segment is rotated about the origin by `pi`, translated vertically by `2`, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

`(9,6)to(-9,4),(5,3)to(-5,1)`

Explanation:

Since there are 3 transformations to be performed, name the endpoints A(9 ,6) and B(5 ,3). This will enable us to 'track' the position of the points after each transformation.

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

a point (x ,y) → (-x ,-y)

hence A(9 ,6) → A'(-9 ,-6) and B(5 ,3) → B'(-5 ,-3)

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

a point (x ,y) → (x ,y+2)

hence A'(-9 ,-6) → A''(-9 ,-4) and B'(-5 ,-3) → B''(-5 ,-1)

Third transformation Under a reflection in the x-axis

a point (x ,y) → (x ,-y)

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

Thus after the 3 transformations.

`(9,6)to(-9,4)" and " (5,3)to(-5,1)`