Question 4
Let $A,B,C$ be three noncollinear points. For each point $M$ in their plane, reflect $M$ in line $AB$ to obtain $M_1$, reflect $M_1$ in line $BC$ to obtain $M_2$, and reflect $M_2$ in line $CA$ to obtain $M'$. Determine all points $M$ for which $MM'$ is least, and call this least distance $d$. Prove that any other order of the three reflections, producing $M''$, has the same least possible distance $MM''=d$.
The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.
The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.