$P(0, 1/2)$,$Q(1/2, 1/2)$,and $R(1/2, 0)$ are respectively the midpoints of sides $\overline{AB}$,$\overline{BC}$,and $\overline{CA}$ in $\Delta ABC$. Find the coordinates of $A$,$B$,and $C$.

(A) Let $A(x_1, y_1)$,$B(x_2, y_2)$,and $C(x_3, y_3)$ be the vertices of $\Delta ABC$. Given that $P(0, 1/2)$,$Q(1/2, 1/2)$,and $R(1/2, 0)$ are the midpoints of sides $\overline{AB}$,$\overline{BC}$,and $\overline{CA}$ respectively.
For $x$-coordinates:
$(x_1 + x_2)/2 = 0 \implies x_1 + x_2 = 0$ $(i)$
$(x_2 + x_3)/2 = 1/2 \implies x_2 + x_3 = 1$ (ii)
$(x_3 + x_1)/2 = 1/2 \implies x_3 + x_1 = 1$ (iii)
Adding $(i)$,(ii),and (iii): $2(x_1 + x_2 + x_3) = 2 \implies x_1 + x_2 + x_3 = 1$.
Subtracting (ii) from the sum: $x_1 = 1 - 1 = 0$.
Subtracting (iii) from the sum: $x_2 = 1 - 1 = 0$.
Subtracting $(i)$ from the sum: $x_3 = 1 - 0 = 1$.
For $y$-coordinates:
$(y_1 + y_2)/2 = 1/2 \implies y_1 + y_2 = 1$ (iv)
$(y_2 + y_3)/2 = 1/2 \implies y_2 + y_3 = 1$ $(v)$
$(y_3 + y_1)/2 = 0 \implies y_3 + y_1 = 0$ (vi)
Adding (iv),$(v)$,and (vi): $2(y_1 + y_2 + y_3) = 2 \implies y_1 + y_2 + y_3 = 1$.
Subtracting $(v)$ from the sum: $y_1 = 1 - 1 = 0$.
Subtracting (vi) from the sum: $y_2 = 1 - 0 = 1$.
Subtracting (iv) from the sum: $y_3 = 1 - 1 = 0$.
Thus,the vertices are $A(0, 0)$,$B(0, 1)$,and $C(1, 0)$.