Parallelograms have to pairs of parallel sides.  It is important to recognize that parallel lines have matching slopes.  To calculate a slope, m, you find the "rise over run."  In other words, you calculate the change in the y-coordinate, and divide that by the change in the x-coordinate between two points.

Step 1: Determine the slope between pairs of the given points, PQ and QR.

For PQ, slope = (4-(-3))/(-2-(-6))=7/4

For QR, slope = (10-4)/(2-(-2))=6/4=3/2

Step 2: Identify the requirements of Point S

In order to form a parallelogram, we need the following:

slope of RS = slope of PQ = 7/4

slope of PS = slope of QR = 3/2

Step 3: Let x denote the x-coordinate of point S, and y denote the y-coordinate of point S.  This allows us to set up a system of equations using the slope requirements.

7/4 = (10-y)/(2-x)

3/2 = (-3-y)/(-6-x)

Step 4: Solve the system of equations.  Start by solving each equation for y:

y=6.5 + 1.75x

y=6 + 1.5 x

Solve by graphing, addition, or substitution to find the solution x = -2, y = 3.

Therefore, Point S is located at (-2, 3).

You can graph this point with the others to see that they do, indeed, form a parallelogram.