Question

求证：顺次连接A(2,-3),B(5,-3.5),C(2,3),D(-4,4)四点所得的是边形是梯形.

Answer 1

线段AD的斜率k1=(4+3)/(-4-2)=-7/6；线段BC的斜率k2=(3+3.5)/(2-5)=-13/6；所以AD和BC不平行；线段AB的斜率k3=(-3+3.5)/(2-5)=-1/6；线段CD的斜率k4=(3-4)/(2+4)=-1/6；所以AB和CD平行；所以四边形ABCD为梯形,AB和CD分别为上下底,AD和BC为腰.