ABCD is a rectangle in the clockwise direction. The coordinates of A are (1,3) and the coordinates of C are (5,1), the coordinates of vertices B and D satisfy the line $$y=2x+c$$, then what will be the coordinates of the mid-point of BC.
Midpoint of AC passes through the line y = 2x + c
Midpoint of AC = (3,2)
2 = 6 + c
c = -4
Line passing through B is y = 2x - 4
(slope of AB)(slope of BC) = -1
$$\left(\ \frac{\ y-1}{x-5}\right)\left(\ \frac{\ y-3}{x-1}\right)=-1$$
Substituting y = 2x - 4 and solving, we get
B(2,0) or B(4,4)
B cannot lie on X-axis. Therefore, co-ordinates of B = (4,4)
Midpoint of BC = $$\left(\frac{9}{2},\frac{5}{2}\right)$$
The answer is option B.
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