If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, then the value of p is:
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Question

If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, then the value of p is:

Accepted Answer

The diagonals of a parallelogram bisect each other. Therefore, the midpoint of diagonal AC must be equal to the midpoint of diagonal BD. Midpoint of AC = $\left(\frac{6 + 9}{2}, \frac{1 + 4}{2}\right) = \left(\frac{15}{2}, \frac{5}{2}\right)$. Midpoint of BD = $\left(\frac{8 + p}{2}, \frac{2 + 3}{2}\right) = \left(\frac{8 + p}{2}, \frac{5}{2}\right)$. Equating the x-coordinates: $\frac{15}{2} = \frac{8 + p}{2} \implies 15 = 8 + p \implies p = 7$. Therefore, the correct option is B.

Coordinate Geometry

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