# Proofs in coordinate geometry

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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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
$AB=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$