Question

a translation slides the figure to a different location.
use a reflection to turn shape 1 into shape 2. this image shows a reflection. reflect the shape across a vertical line.
use a translation to turn shape 2 into shape 3. this image shows a translation. translate the shape up 6 and right 1.
to go from shape 1 to shape 2 to shape 3, use a reflection and then a translation.

Explanation:

Step1: Reflect Shape 1

To reflect Shape 1 (green) across the vertical red line, find the mirror image of each vertex of Shape 1 with respect to the vertical line. For a vertical line of reflection, the x - coordinate of each point \((x,y)\) is transformed to \((-x + 2h,y)\) where \(h\) is the x - coordinate of the vertical line. This will give us Shape 2 (blue).

Step2: Translate Shape 2

To translate Shape 2 (blue) to Shape 3 (purple), move each vertex of Shape 2 up by 6 units (increase the y - coordinate by 6) and then right by 1 unit (increase the x - coordinate by 1).

Answer:

To transform Shape 1 to Shape 2 to Shape 3, first reflect Shape 1 across the given vertical line to get Shape 2, then translate Shape 2 6 units up and 1 unit right to get Shape 3. The transformations are a reflection (across vertical line) followed by a translation (up 6, right 1).