Question

Assertion (A): If the points \(\mathrm{A}(x, 1), \mathrm{B}(8, 2), \mathrm{C}(9, 4)\) and \(\mathrm{D}(7, 3)\) are the vertices of a parallelogram, taken in order, then the value of x is 6.

Reason (R): Adjacent angles of a parallelogram are supplementary.

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

Both A and R are true, but R is not the correct explanation of A.

Explanation:

Diagonals of a parallelogram bisect each other, so midpoints of AC and BD are equal: $$\left(\frac{x + 9}{2}, \frac52\right) = \left(\frac{15}{2}, \frac52\right) \Rightarrow x = 6.$$

Thus A is true. R is also true, but it does not explain why x = 6.