There is a plane $\alpha$ in coordinate space. Let $\mathrm{A}'$ and $\mathrm{B}'$ be the orthogonal projections of two distinct points $\mathrm{A}$ and $\mathrm{B}$ (not on plane $\alpha$) onto plane $\alpha$, respectively. $$\overline{\mathrm{AB}} = \overline{\mathrm{A'B'}} = 6$$ Let $\mathrm{M}'$ be the orthogonal projection of the midpoint M of segment AB onto plane $\alpha$. A point P is chosen on plane $\alpha$ such that $$\overline{\mathrm{PM'}} \perp \overline{\mathrm{A'B'}}, \quad \overline{\mathrm{PM'}} = 6$$ When the area of the orthogonal projection of triangle $\mathrm{A'B'P}$ onto plane ABP is $\frac{9}{2}$, what is the length of segment PM? [3 points] (1) 12 (2) 15 (3) 18 (4) 21 (5) 24
There is a plane $\alpha$ in coordinate space. Let $\mathrm{A}'$ and $\mathrm{B}'$ be the orthogonal projections of two distinct points $\mathrm{A}$ and $\mathrm{B}$ (not on plane $\alpha$) onto plane $\alpha$, respectively.
$$\overline{\mathrm{AB}} = \overline{\mathrm{A'B'}} = 6$$
Let $\mathrm{M}'$ be the orthogonal projection of the midpoint M of segment AB onto plane $\alpha$. A point P is chosen on plane $\alpha$ such that
$$\overline{\mathrm{PM'}} \perp \overline{\mathrm{A'B'}}, \quad \overline{\mathrm{PM'}} = 6$$
When the area of the orthogonal projection of triangle $\mathrm{A'B'P}$ onto plane ABP is $\frac{9}{2}$, what is the length of segment PM? [3 points]\\
(1) 12\\
(2) 15\\
(3) 18\\
(4) 21\\
(5) 24