From a point on the original object measure the perpendicular distance to the mirror line
Continuing from that point on the mirror line, and in the same direction, measure the same distance again
Mark the corresponding point on the reflected image at the position you have reached
1. Vertical lines (of the form , for some number )
2. Horizontal lines (of the form , for some number )
3. Diagonal lines (of the form , see straight line graphs)
4. Double Reflections
5. Regular polygons
Draw in the mirror line, it has a gradient of 1 and intercepts the y-axis at (0, 3).
It is a diagonal line so you need to be careful and reflect one vertex at a time before drawing in the final reflected object.
Because it has a gradient of 1, you can count the "diagonals" from each vertex to the mirror line, as this is the perpendicular distance.
Count the same number of "diagonals" on the other side of the mirror line to find the position of the corresponding vertex on the reflected image.
List the vertices of the reflected image.
Work your way around the shape vertex by vertex so that you don't miss any out as there are quite a few!
Vertices of the reflected shape: (0, 0), (3, 0), (3, -1), (1, -1), (1, -2), (3, -2), (3, -3), (0, -3), (-2, -2), (-2, -1), (0, -1)
You should be able to "see" where the mirror line should be without too much difficulty.
Draw the mirror line on the diagram.
You can check that it is in the correct position by measuring/counting the perpendicular distance from a pair of corresponding points on the original object and the reflected image to the same point on the mirror line.
Be careful with mirror lines near axes as it is easy to miscount.
Write down that the transformation was a reflection and the equation of the mirror line.
Shape A has been reflected in the line to create shape B