Math, asked by prasadghole781, 7 months ago

If A( -2, -1) , B( p,0), C( 4,q) and D( 1,2) are the vertices of a parallelogram, find the values of p and q.​

Answers

Answered by Ataraxia
55

Solution :-

Given :-

The points A ( -2 , -1 ), B ( p , 0 ), C ( 4 , q )and D ( 1 , 2 ) are the vertices of a parallelogram.

We know :-

The diagonals of the parallelogram bisects each other.

That is,

Midpoint of diagonal AC = Midpoint of diagonal BD

\boxed{\sf Midpoint \ formula = \left( \dfrac{x_1+x_2}{2} \ ,  \ \dfrac{y_1+y_2}{2} \right)}

\implies \sf \left( \dfrac{-2+4}{2} \ , \ \dfrac{-1+q}{2} \right)= \left( \dfrac{1+p}{2} \ , \ \dfrac{2+0}{2} \right)

\longrightarrow \sf \dfrac{-2+4}{2}=\dfrac{1+p}{2} \\\\\longrightarrow \dfrac{2}{2} = \dfrac{1+p}{2} \\\\\longrightarrow 1 = \dfrac{1+p}{2} \\\\\longrightarrow 1+p = 2 \\\\\longrightarrow\bf  p = 1

\longrightarrow \sf \dfrac{-1+q}{2} =\dfrac{2+0}{2} \\\\\longrightarrow \dfrac{-1+q}{2} = \dfrac{2}{2} \\\\\longrightarrow \dfrac{-1+q}{2} = 2 \\\\\longrightarrow -1+q = 2 \\\\\longrightarrow \bf q = 3

Value of p = 1

Value of q = 3

Answered by meenagotiwale
8

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