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The coordinates (1,3) and (5,1) represent a pair of opposite corners of a rectangle. If the other two corners lie on the straight line y = 2x + c, then one of those corners is

1. (4,4)
2. (2,2)
3. (0,2)
4. (4,2)

Correct answer: (4,4)

Solution

Centre = midpoint (3,2); the line through the other corners passes through it, so c=-4 (y=2x-4). Intersecting with the circle (x-3)^2+(y-2)^2=5 gives (2,0) and (4,4); (4,4) is listed.

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