Geometry
# Isometries

$\lvert \overline{AB} \rvert = 9, \lvert \overline{BC} \rvert = 3,$$\lvert \overline{CD} \rvert = 3, \lvert \overline{DE} \rvert = 3.$ If the shape is flipped across the line segment $\overline{AE}$ to complete a house, what will be the perimeter of the house?

The lengths of the lines in the above figure (a half house) are as follows:$ABCD$ in the above graph is reflected in the line $y = -1,$ what is the image of point $D?$ The side length of each square in the graph paper is $1.$

If rectangle$B$ on the right is the reflection of shape $A$ in the red line. Given the following numbers: $L = 48, \quad N = 3, \quad M = 6$ in the diagram, what is the value of $a - b + c - d?$

In the above diagram, shape