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Rectangle with opposite vertices (1, 3) and (5, 1), other two vertices on y = 2x + c: find them

The same question, asked 2 times: 10 May 2024 S1, 21 Apr 2025 S2. Every wording below, oldest first.

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  1. Question 1

    10 May 2024 S1

    133
    (1,3) and (5,1) are opposite vertices of a rectangle. Other two vertices lie on y=2x+c. One vertex on other diagonal is

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  2. Question 2

    21 Apr 2025 S2

    148
    The points (1,3)(1,3) and (5,1)(5,1) are two opposite vertices of a rectangle. The other two vertices are lie on the line y=2x+cy= 2x+ c where c is the constant, then co-ordinates of other two vertices are

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