Question

If A=(2, 3), B = (-1, 0), C = (4, 6) then area of the parallelogram ABCD is:

• A. 3
• B. \(\frac{3}{2}\)
• C. 6
• D. 2

Answer 1

The Correct Option is A

To find the area of the parallelogram ABCD with vertices A, B, C, and D, we can use the concept of the cross product of vectors. The area of the parallelogram formed by vectors \(\overrightarrow{AB}\) and \(\overrightarrow{AC}\) is given by the magnitude of their cross product.

First, find the vectors:

• \(\overrightarrow{AB} = B - A = (-1 - 2, 0 - 3) = (-3, -3)\)
• \(\overrightarrow{AC} = C - A = (4 - 2, 6 - 3) = (2, 3)\)

Now, calculate the determinant which gives the magnitude of the cross product:

\[\text{Area} = \left| \begin{vmatrix} -3 & -3 \\ 2 & 3 \end{vmatrix} \right| = \left|(-3)(3) - (-3)(2)\right| = | -9 + 6 | = 3\]

Therefore, the area of the parallelogram ABCD is 3.