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The equation of the diagonal line is $y-y_1=\frac{y_1-y_2}{x_1-x_2}(x-x_1)$, i.e. $y=\frac{y_1-y_2}{x_1-x_2}(x-x_1)+y_1$ So, the $x$ coordinate of the upper point satisfies $$75=\frac{y_1-y_2}{x_1-x_2}(x-x_1)+y_1$$ and the $x$ coordinate of the lower point satisfies $$25=\frac{y_1-y_2}{x_1-x_2}(x-x_1)+y_1.$$ Now you can solve these for $x$.


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I assume that, as in the question you linked to, the rectangle can have any orientation and is not limited to horizontal/vertical sides. There are infinitely many rectangles that have two given points as opposite vertices: a third vertex can be any point on the circle that has those two points as the ends of a diameter. A point outside that circle will be ...


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Let me try to answer this question. According to H.R. Tiwary, "On the hardness of computing intersection, union and Minkowski sum of polytopes". Discrete & Computational Geometry, p. 469–479, 2008 the problem of enumerating all rows of the matrix representing $H_1\oplus H_2$ is NP-hard. So: No, there is no explicit relation between the ...


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It is the d-dimensional (real) euclidean hyper-plane $\mathbb{R}^d$



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