Question

If \(A (2,3), B(2,4) C(4,9)\)and \(D (x,8)\) are the vertices of a parallelogram \(ABCD\), then find the value of \(x.\)

• A. 8
• B. 16
• C. 5
• D. 4

Answer 1

The Correct Option is D

If \(A(2,3), B(2,4), C(4,9),\) and \(D(x,8)\) are the vertices of a parallelogram \(ABCD\), then we need to find the value of \(x\).

In a parallelogram, the diagonals bisect each other. Therefore, the midpoint of diagonal \(AC\) will be equal to the midpoint of diagonal \(BD.\)

The midpoint of \(AC\) is calculated as follows:

\[\left(\frac{2+4}{2},\frac{3+9}{2}\right)=\left(3,6\right)\]

The midpoint of \(BD\) is calculated as follows:

\[\left(\frac{2+x}{2},\frac{4+8}{2}\right)=\left(\frac{2+x}{2},6\right)\]

Equating the two midpoints, we have:

\[3=\frac{2+x}{2}\]

Solving for \(x\), we multiply both sides by 2:

\[6=2+x\]

Subtracting 2 from both sides gives:

\[x=4\]

Therefore, the value of \(x\) is 4.