The coordinates of quadrilateral pqrs are p(0, 0), q(a + c, 0), r(2a + c, b), and s(a, b). how can you use coordinate geometry to show that one pair of opposite sides is parallel?

We will use the formula for the slope:
m = ( y2- y1 ) / ( x2 - x1 )
For PQ : m = ( 0 - 0 ) / ( a + c - 0 ) = 0
For RS : m = ( b - b ) / ( a - ( 2a + c )) = 0
Both slopes are m = 0, so PQ and RS are parallel to x - axis and at the same time parallel to each other ( PQ | | RS ). One pair of opposite sides is parallel.