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Given a parallelogram RSTU in a coordinate plane, where:

  • R = (b,c)
  • S = (a + b, c)
  • T = (a, 0)
  • U = (0,0)

the statement $ \sqrt{(b - 0)^2 + (c - 0)^2} = \sqrt{(b +a - a)^2 + (c-0)^2}$ would be used to prove...what?

I thought it would be used to prove that opposite sides were congruent, since when not simplified they both represent the $x\_coord + y\_coord$ of one point minus the $x\_coord + y\_coord$ of the point underneath it.

Is this correct?

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up vote 0 down vote accepted

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The formula they are using is euclidean distance.It is used to find out distance between two points.$A(x_1,y_1)$ and $B(x_2,y_2)$ are points then distance between these two points are


and you are correct in your last statement.

So in this question since this is a parallelogram there are RS=UT and UR=TS and they apply euclidean formula on UR=TS. this will helpful

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