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Question 1162029: A quadrilateral ABCD is formed by the points A(-3,2),B(4,3),C(9,-2) and D(2,-3)
(a)show that all four sides are equal in length
(b)show that ABCD is not a square
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A quadrilateral ABCD is formed by the points
A(-3,2),B(4,3),C(9,-2) and D(2,-3)
(a)show that all four sides are equal in length
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It's important the the points are in order around the figure.
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Find the 4 lengths.
For AB: d^2 = diffy^2 + diffx^2 = (-3-4)^2 + (2-3)^2
Finding d^2 is sufficient, taking the sq root is not necessary.
Do the same for BC, CD and DA.
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(b)show that ABCD is not a square
2 ways to do this:
Find the slopes of AB, BC, CD and DA
Iff adjacent sides are perpendicular, it's a square.
o/w not.
PS Iff = if and only if
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Find the distances AC and BD.
IFF they're equal, it's a rectangle, and if the sides are equal it's a square.
Answer by solver91311(24713)  (Show Source):
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