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The points (1,3) and (5,5) are opposite vertices of a rectangle. The other two vertices lie on the y=2x + k. Find the value of k.

I don't think that the remaining vertices lie on y = 2x + k.  They should lie on the equation with negative slope, because the remaining vertices are opposite, therefore, the line where they lie crosses the diagonal connecting the given opposite vertices. 
Opposite vertices are different from adjacent vertices (same side).
I'll try. 
I thin I got it :-)


Given the points (1,3) and (5,5) as the opposite vertices of a rectangle in Cartesian place, the other two (opposite) vertices lie on:

y = - ¹/₂ x + 11/2

To prove that y = 2x + k is not the equation where the two remaining (opposite) vertices lie, please CLICK  the image below with illustration and explanation.  Thanks.
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