Question

A line segment has endpoints at `(1 ,6 )` 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

See explanation.

Explanation:

The starting points' coordinates are:

`A=(1,6)`

and

`B=(5,1)`

I step - rotate about origin.

Rotating about origin by `pi` is equal to a symetry about the origin which changes the sign of both coordinates to opposite numbers, so the new coordinates are:

`A_1=(-1,-6)`

and

`B_1=(-5,-1)`

II step - translation

Translating horizontally by `-4` means subtracting `4` from `x` coordinates.

`A_2=(-5,-6)`

and

`B_2=(-9,-1)`

II step - reflect about `Y` axis.

Reflecting about `Y` axis means changing `X` coordinate to opposite.

`A_3=(5,-6)`

and

`B_3=(9,-1)`

Finally we can say that the new coordinates are:

`A_3=(5,-6)` and `B_3=(9,-1)`