SAT数学题求翻译及解题过程Rectangle ABCD lies in the xy-coordinate plane so that its sides are not parallel to the axes. What is the product of the slopes of all four sides of rectangle ABCD?(A) -2 (B) -1 (C) 0 (D) 1 (E) 2

Question

SAT数学题求翻译及解题过程
Rectangle ABCD lies in the xy-coordinate plane so that its sides are not parallel to the axes. What is the product of the slopes of all four sides of rectangle ABCD?
(A) -2 (B) -1 (C) 0 (D) 1 (E) 2

Answer 1

xy坐标系中的矩形ABCD,其边与坐标轴均不平行.四条边的斜率乘积是多少?
矩形么,四条边有以下的关系
AB⊥BC,CD⊥DA
这个表示
AB的斜率 x BC的斜率应该为 -1,CD的斜率 x DA的斜率也应该为 -1,
即 如果AB的斜率是 s,那么BC的斜率一定是 -1/s
那么两个-1相乘就是1咯,选D