Question

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

Answer 1

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.
Since, the midpoint of the line segment joining the two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.
$\therefore$ $(\frac{6+9}{2},\frac{1+4}{2})$ = $(\frac{8+p}{2},\frac{2+3}{2})$

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

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

$\Rightarrow$ 15 = 8+p

$\Rightarrow$ P = 7