Question

If the point A ( -2,-1) B ( 1,0) C ( p, 3) D(1,q) from the parallelogram ABCD find the value of p and q

Answer 1

Hiiii friend,

A(-2,-1) , B(1,0) , C(P,3) and D(1,Q) are the vertices of a parallelogram ABCD.

Join AC and BD , interesting each other at the point O.

We know that,

Diagonals of a parallelogram bisect each other.

A(-2,-1) and C(P,3)

Here,

X1 = -2 , Y1 = -1 and X2 = P , Y2 = 3

Therefore,



Midpoint of AC is (X1+X2/2 , Y1+Y2/2) = (-2+P/2 , -1+3/2) = (-2+P/2 , 2/2) = (-2+P/2 , 1).




B(1,0) and D(1,Q)

Here,

X1 = 1 , Y2 = 0 and X2 = 1 , Y2 = Q


Therefore,



Midpoint of BD is ( X1+X2/2 , Y1+Y2/2) = (1+1/2 , 0+Q/2) = (2/2 , Q/2) = (1,Q/2).


But,

These points coincide at the point O.

Therefore,

(-2+P/2) = 1 And Q/2 = 1


-2+P = 2 And Q = 2

P = 2+2 And Q = 2


P = 4 AND Q = 2.


HENCE,


P = 4 AND Q = 2.

HOPE IT WILL HELP YOU....... :-)

Answer 2

Answer:

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