anonymous
  • anonymous
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?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
(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
anonymous
  • anonymous
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?
anonymous
  • anonymous
this is urgent! someone please help!

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hartnn
  • hartnn
@Australopithecus @SolomonZelman @surjithayer @mathmate @misty1212 can anyone of you please help this user? thanks.
mathmate
  • mathmate
Each option represents the product of the slopes of adjacent sides of two adjacent angles.|dw:1435032545515:dw| 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.

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