Question

The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if parallelogram ABCD is proven to be a rectangle?

A- (y4−y3x4−x3=y3−y2x3−x2) and (y4−y3x4−x3×y3−y2x3−x2)=-1

B- (y4−y3x4−x3=y2−y1x2−x1) and (y4−y3x4−x3×y2−y1x2−x1)=-1

C- (y4−y3x4−x3=y2−y1x2−x1) and (y4−y3x4−x3×y3−y2x3−x2)=-1

D- (y4−y3x4−x3=y3−y1x3−x1) and (y4−y3x4−x3×y2−y1x2−x1)=-1

Answer 1

you are asking for the condition needed for the 
two segments to be perpendicular to each other. 

If the slope of one segment is m, then the slope of a perpendicular segment would be -1/m 

this means that m2 = -1/m and so m2 x m = -1 

If you look carefully at your choices, the 3rd answer involves the two slope and has the -1. It's 
the correct answer.

Answer 2

(y4−y3x4−x3=y2−y1x2−x1) and (y4−y3x4−x3×y3−y2x3−x2)=-1