Question

the points A(1,-2), B(2,3) ,C(k,2) ,D(-4,-3) are the vertices of a parallelogram find the value of 'k and the altitude of the parallelogram corresponding to the base AB can we do this with distance formula??

Answer 1

Answer:

Step-by-step explanation:

we know that,

                       Diagonals of a parallelogram bisect each other at point of                          

                        intersection.

=> midpoint of AC = midpoint of BD

=> (1+k/2 , -2+2/2) = (2-4/2 , 3-3/2)

     1+k/2 = 2-4/2

     1+k -2*2/2

      1+k = -4/2

      k = -2-1

      k = -3

Answer 2

Answer:

Given :

Vertices of a parallelogram are A ( 1 , - 2 ) , B ( 2 , 3 ) , C ( k , 2 ) and D ( - 4 , - 3 ).

We know Diagonal of parallelogram bisect each other .

Midpoint of AC = mid point of BD

= > ( 1 + k / 2 , -2 + 2 / 2 ) = ( - 4 + 2 / 2 , - 3 + 3 / 2 )

= > 1 + k / 2 = - 2 / 2

= > 1 + k = - 2

= > k = - 3 .

Therefore , the value of k is - 3 .