Discussion

Question:

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.

Explanation:

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

$(\frac{y - 1}{x - 5})$ $(\frac{y - 3}{x - 1})$ = -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 = $(\frac{9}{2}, \frac{5}{2})$

The answer is option B.

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