# 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?

Nov 24, 2017

See explanation.

#### Explanation:

The starting points' coordinates are:

and

## $B = \left(5 , 1\right)$

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:

and

## ${B}_{1} = \left(- 5 , - 1\right)$

II step - translation

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

and

## ${B}_{2} = \left(- 9 , - 1\right)$

II step - reflect about $Y$ axis.

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

and

## ${B}_{3} = \left(9 , - 1\right)$

Finally we can say that the new coordinates are:

${A}_{3} = \left(5 , - 6\right)$ and ${B}_{3} = \left(9 , - 1\right)$