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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

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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

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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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