Question

2.15: 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,
find the value of p​

Answer 1

Answer:

$\large{\pink{ \textbf{P = 7}}}$

To Find :

• value of p = ?

DIAGRAM :

$\setlength{\unitlength}{1.3cm}\begin{picture}(8,2)\thicklines\put(8,3){\large{A (6,1)}}\put(7.5,0.7){\large{D (p,3)}}\put(11.1,0.9){\large{C (9,4)}}\put(9.9,2.1){\large{O}}\put(8,1){\line(1,0){3}}\put(11,1){\line(1,2){1}}\put(9,3){\line(3,0){3}}\put(11,1){\line(-1,1){2}}\put(8,1){\line(2,1){4}}\put(8,1){\line(1,2){1}}\put(12.1,3){\large{B (8,2)}}\end{picture}$

Step-by-step explanation:

O is the mid point of AC and BD {Diagonal of parallelogram bisect each other}

1) Finding mid point of AC

x coordinate of O = $\sf \dfrac{x_1 + x_2}{2}$

Where, $\sf x_1=6$ and $\sf x_2 = 9$

$\leadsto\:$$\sf \dfrac{6 + 9}{2}$

$\leadsto\:$$\sf \dfrac{15}{2}----(1)$

2) Finding mid point of BD

x coordinate of O = $\sf \dfrac{x_1 + x_2}{2}$

Where, $\sf x_1=8$ and $\sf x_2=p$

$\leadsto\:$$\sf \dfrac{8+p}{2}----(2)$

Comparing equation (1) and (2), we get :

$\leadsto\:$$\sf \dfrac{15}{2} = \dfrac{8+p}{2}$

$\leadsto\:$$\sf 15 = 8+p$

$\leadsto\:$$\sf p = 15 - 8$

$\leadsto\:$$\sf p = 7$

Therefore, value of p is 7.