# geometry

prove the following statements using a coordinate proof.

the diagonals of a rectangle bisect each other.

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1. Choose a rectangle with arbitrary side lengths a and b. The proof will be easier if you locate one corner at the origin (0,0). Let a be the length of the side on the x axis

Derive equations for the two diagonals.
One equation will be y1 = (b/a)x
The other will be y2 = b -(b/a)x

Set the two equations equal to get the intersection point
y1 = y2 where (b/a)x = -(b/a)x + b
2(b/a) x = b
x = a/2
y = b/2
That's clearly the midpoint of the diagonals

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2. Hag

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