geometrytransformationsdesmos

Reflection Over a Line

Visualizing geometric reflection with an interactive graph

February 28, 2026 3 min read

P_{ref} = P - 2\frac{(P-P_0)\cdot n}{\|n\|^2}n

In this post, we visualize how a point reflects across a line.

For a line with point $P_{0}$ and normal vector $n$ , the reflected point of $P$ is:

P^{'} = P - 2 \frac{( P - P _{0} ) \cdot n}{∥ n ∥ ^{2}} n