Question
Show that points A (1, 2, 3), B (-1, -2, -1), C (2, 3, 2) and D (4, 7, 6) are the vertices of a parallelogram ABCD, but it is not a rectangle.
Solution
Using distance formula, we have
...(i)
...(ii)
...(iii)
...(iv)
From (i), (ii), (iii) and (iv), AB = CD, BC = DA
∴ ABCD is a parallelogram.
Also,
...(v)
...(vi)
From (v) and (vi), we have
Hence, ABCD is a parallelogram, but not a rectangle.
...(ii)
...(iii)
...(iv)
From (i), (ii), (iii) and (iv), AB = CD, BC = DA
∴ ABCD is a parallelogram.
Also,
...(v)
...(vi)
From (v) and (vi), we have
Hence, ABCD is a parallelogram, but not a rectangle.