Exercise 9 Page 577

To graph a reflection image in a line, we need to follow three steps.

1. Graph the preimage and identify the line of reflection on the coordinate plane.
2. Locate the image of each vertex so that the reflection line is the perpendicular bisector of the segment between the vertex and its image.
3. Connect the new vertices to draw the image of the given figure.

Let's do it!

Step $1$

We will begin by plotting the given vertices and graphing the figure. Since we want to reflect the given figure across the line $x=\text{-}1,$ we will identify it as the line of reflection.

Step $2$

Now we will locate the image of each vertex so that the line $x=\text{-}1$ is the perpendicular bisector of the segment between the vertex and its image. The distance between the image vertex and the $x=\text{-}1$ must be the same as the distance between the preimage vertex and the $x=\text{-}1.$ This is shown for vertex $B$ below.

If you need further explanation on how to draw a line that passes through a given point and is perpendicular to a given line, please refer to this explanation.

Step $3$

Finally, we can connect the new vertices to draw the reflection image of the given figure.