Below are two lines $(D)$ and $(\Delta)$. We are given a point $M$ on $(D)$ and its reflection wtr $(\Delta)$. If $A$ is another point on $(D)$, it is asked to construct the reflection of it wtr $(\Delta)$ Using straightedge only.
I tried to use $J = (AN)\cap (\Delta)$ but in vain
Usually in Ruler & Compass constructions we can draw a parallel to a given straight line through another point not on it using a compass. If this is allowed,
draw a line parallel to MN through A (red), another line parallel to MA through N (blue) intersecting at P, the required image of A.
If Compass not allowed, can a Set square used by engineers/draftsmen be allowed ? If so, another known procedure to draw parallels:
One edge of a set square is aligned to the given line, another edge is made to slide on another edge till it goes through the given point, to draw parallel lines...in both cases.
