See Fig.Equation of the line AC is
y - 4 = 4 + 1/3 - 1(x - 3)
2y - 8 = 5x - 15
5x - 2y - 7 = 0
Its slope is 5/2. Let the slope of side CD be m. Then
Therefore, equations of CB and CD are
Similarly, the equations of AB and BD, respectively, are
Therefore, the equations of the sides are 3x − 7y − 10 = 0,
7x + 3y − 4 = 0, 3x − 7y − 19 = 0 and 7x + 3y − 33 = 0
Aliter (Using Complex Numbers): Let A = 3 + 4i, C = 1 − i, M = midpoint of AC = 2 + 3/2i. Let B denote Z. Rotate (bar)MA about M through 90° in the anticlockwise sense so that
Now, we can write the sides equations because the vertices are obtained as A(3, 4), B(−1/2, 5/2), C(1, −1), D(9/2, 1/2).