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Geometry of Equations

Review question

Can we find the coordinates of this tilted rectangle?
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Ref: R6366

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Question

In the rectangle \(ABCD\), \(A\) and \(B\) are the points \((4,2)\) and \((2,8)\) respectively.

Graph with the rectangle ABCD. A and B are on the left-facing side of the rectangle, C is the top-right vertex, and D is the bottom-right

Given that the equation \(AC\) is \(y=x-2\), find

the equation of \(BC\),
the coordinates of \(C\),
the coordinates of \(D\),
the area of the rectangle \(ABCD\).

This question needs an exact method that goes beyond accurate drawing.