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

Sum

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

#### Solution

We know that the diagonals of a parallelogram bisect each other. So, coordinates of the mid-point of diagonal AC are same as the coordinates of the mid-point of diagonal BD.

\therefore ( \frac{6+9}{2},\ \frac{1+4}{2})=(\frac{8+p}{2},\ \frac{2+3}{2})

\Rightarrow ( \frac{15}{2},\ \frac{5}{2})=( \frac{8+p}{2},\ \frac{5}{2})

\Rightarrow \frac{15}{2}=\frac{8+p}{2}

⇒ 15 = 8 + p

⇒ p = 7

Concept: Section Formula
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