Question 490711: Assignment:
Proove the points A(6,-13) B(-2,2) C(13,10) and D (21, -5) are the vertices of the square. Show that the diagonals bisect each other and of equal length. Please have a plan of what you're going to do before proceeding into solving the problem.
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Hello! How am I going to solve this problem? Am I going to get their distances and midpoints? Please help me. Thank you :)
Found 2 solutions by richard1234, josmiceli:
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! First, you can show that AB, BC, CD, and DA are all of equal length. For example,
^2 + (2 - (-13))^2})
However this only proves that the quadrilateral is a rhombus. To prove it is a square, you could perhaps show that one of the angles is 90, then it will follow that the quadrilateral is a square.
Take the slope of two segments. For example, the slope of line AB is
}{-2 - 6} = \frac{15}{-8})
and the slope of BC is
} = \frac{8}{15})
Hence, AB and BC are perpendicular, and it follows that ABCD is a square.
Answer by josmiceli(19441)  (Show Source):
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