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?

Answer 1

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

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

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

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

Answer 2

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?

Answer 3

this is urgent! someone please help!

Answer 4

@Australopithecus @SolomonZelman @surjithayer @mathmate @misty1212

can anyone of you please help this user?
thanks.

Answer 5

Each option represents the product of the slopes of adjacent sides of two adjacent angles.
If ABCD is given to be a parallelogram, we only need to prove one angle to be 90 degrees, although the options attempt to show
1. AB is parallel to CD, and
Slope of AB, m1 = (y2-y1)/(x2-x1)
Slope of CD, m3 = (y4-y3)/(x4-x3)
If AB is parallel to CD, then m1=m3.

2. Angle BCD = 90 degrees
To show 90 degrees, we need to show the products of the slopes of adjacent sides equals -1.
Slope of CD, m3= (y4-y3)/(x4-x3)
Slope of BC, m2= (y3-y2)/(x3-x2)
If (m2*m3)=-1, then angle BCD=90 degrees.

So select the correct option that achieves the above.
By the way, there are probably typos in the answer options, I believe they should read:

(y4−y3)/(x4−x3)=(y3−y2)/(x3−x2) and (y4−y3)/(x4−x3×y3−y2)/(x3−x2)=-1

(y4−y3)/(x4−x3)=(y2−y1).(x2−x1) and (y4−y3)/(x4−x3×y2−y1)/(x2−x1)=-1

(y4−y3)/(x4−x3)=(y2−y1)/(x2−x1) and (y4−y3)/(x4−x3×y3−y2)/(x3−x2)=-1

(y4−y3(/(x4−x3)=(y3−y1)/(x3−x1) and (y4−y3)/(x4−x3×y2−y1)/(x2−x1)=-1

Make your choice accordingly.