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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 $x$.


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 ...


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 ...


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

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