Question

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:

Given that ABCD is a parallelogram.

Let co-ordinate A be the (x1,y1), B be the (x2,y2), C be the (x3,y3) and D be the (x4,y4).

We know that diagonals of the parallelogram bisects each other.

So, Mid - point of AC = Mid - point of BD

Mid-point of AC = x1 + x3/2 , y1 + y3/2

= 6 + 9/2 , 1 + 4/2

= 15/2 , 5/2

Mid-point of BD = x2 + x4/2 , y2 + y4/2

= 8 + p/2 , 2 + 3/2

= 8 + p/2 , 5/2

8 + p/2 = 15/2

8 + p = 15

p = 15 - 8

p = 7