If $d[(5,0), (x, 4)] = \sqrt{17}$,then $x = \ldots \ldots \ldots$

State whether the following statement is true or false. Justify your answer.
Points $A(3, 1)$,$B(12, -2)$,and $C(0, 2)$ cannot be the vertices of a triangle.

Given $P-R-Q$ and if $\frac{PR}{PQ} = \frac{2}{7}$,then $R$ divides $\overline{PQ}$ from $Q$ in the internal division ratio $\ldots \ldots \ldots \ldots$

If the points are $(12, 10)$ and $(0, 8)$,then the midpoint of the line segment joining these two points is $\ldots \ldots \ldots \ldots$

Which of the following groups is true for $\square ABCD?$

$1$. $\square ABCD$ is a rhombus.	$a$. $\overline{AC}$ and $\overline{BD}$ bisect each other.
$2$. $\square ABCD$ is a parallelogram.	$b$. $\overline{AC}$ and $\overline{BD}$ bisect each other at right angles.
$3$. $\square ABCD$ is a rectangle.	$c$. $\overline{AC}$ and $\overline{BD}$ are congruent and bisect each other at right angles.
$4$. $\square ABCD$ is a square.	$d$. $\overline{AC}$ and $\overline{BD}$ are congruent and bisect each other.

$P(0, 1/2)$,$Q(1/2, 1/2)$,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 $C$.