SOLUTION: the quadrilateral with vertices P(6,3), Q(2,-2), R(1,7) and S(x,y) is a parallelogram. Find (x,y) algebraically.

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Question 134119: the quadrilateral with vertices P(6,3), Q(2,-2), R(1,7) and S(x,y) is a parallelogram. Find (x,y) algebraically.
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Calculate the slope of the line passing through P and Q. Use the point-slope form of the equation of a line to derive an equation of a line parallel to the line through P and Q passing through R. Hint: Parallel lines have equal slopes.

Repeat the process using the slope of the line through PR to derive an equation of the line parallel to PR passing through Q.

Solve the system of equations consisting of your two derived equations. The solution set will be the ordered pair defining S.