(7,-3),(5,10),(15,7) and (3,5) taken in order are the corners of a parallelogram

The midpoint formula is $M = \left( \frac{x_a + x_b}{2}, \frac{y_a + y_b}{2} \right)$.
$M_{P_1P_3} = \left( \frac{x_1 + 15}{2}, \frac{-3 + 7}{2} \right) = \left( \frac{x_1 + 15}{2}, \frac{4}{2} \right) = \left( \frac{x_1 + 15}{2}, 2 \right)$

$M_{P_2P_4} = \left( \frac{5 + 3}{2}, \frac{10 + y_4}{2} \right) = \left( \frac{8}{2}, \frac{10 + y_4}{2} \right) = \left( 4, \frac{10 + y_4}{2} \right)$

Since the midpoints are the same:
$\frac{x_1 + 15}{2} = 4$
$x_1 + 15 = 8$
$x_1 = 8 - 15$
$x_1 = -7$

$2 = \frac{10 + y_4}{2}$
$4 = 10 + y_4$
$y_4 = 4 - 10$
$y_4 = -6$

The missing coordinates are $x_1 = -7$ and $y_4 = -6$.
The four corners of the parallelogram are $(-7,-3)$, $(5,10)$, $(15,7)$, and $(3,-6)$.

The missing coordinates are:
The x-coordinate of the first point is $\boxed{-7}$.
The y-coordinate of the fourth point is $\boxed{-6}$.