Question

The three vertices of a parallelogram ABCD are : A(-2, 3), B (6, 7) and C (8 , 3) , then the fourth vertex D is
1. 1, 0
2. 0, 1
3. -1, 0
4. 0, -1

Answer 1

Correct Answer - Option 4 : 0, -1

Concept:

The diagonals of a parallelogram bisect each other.

Let A(x1, y1, z1) and B(x2, y2, z2), then midpoint = \(\rm {(x_1\; +\; x_2)\over2},{(y_1\; + \;y_2)\over2}\)

Calculation:

Let, the co-ordinates of D = (x, y)

The midpoint of AC = \(\rm {(-2\;+\;8)\over2},{(3\;+\;3)\over2} = (3,3)\)

The midpoint of BD = \(\rm {(6\;+\;x)\over2},{(7\;+\;y)\over2} \)

As the midpoint of AC and BD is same we can write,

\(\rm {(6\;+\;x)\over2}= 3\)

∴ 6 + x = 6

∴ x = 0

Similarly, \(\rm {(7\;+\;y)\over2}= 3\)

∴ 7 + y = 6

∴ y = -1

So, D(x, y) = (0, -1)