Question

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

Answer 1

`(5,-5)" and " (9,-1)`

Explanation:

Since there are 3 transformations to be performed, label the endpoints A(1 ,5) and B(5 ,1) and note the change in them after each transformation.

`color(blue)"First transformation"` Under a rotation about origin of `"pi`

`• "a point "(x,y)to(-x,-y)`

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

`color(blue)"Second transformation"` Under a translation `((-4),(0))`

`• "a point " (x,y)to(x-4,y)`

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

`color(blue)"Third transformation"` Under a reflection in the y-axis

`• "a point " (x,y)to(-x,y)`

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

Thus after all 3 transformations.

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