Question

If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) taken in order are the vertices of a parallelogram, find the value of p using distance formula.

Answer 1

By using distance formula,
   take two points B(8,2) and D(p,3)
  distance formula is √(x₂-x₁)²+(y₂-y₁)²
   in point B 8 is x₁ and 2 is y₁
   in point D p is x₂ and 3 is y₂
Now,
     =√(p-3)²+(3-2)²
     =√(p-8)²+(1)²
     =p-8+1
     =p-7
   ⇒p=7

Answer 2

Answer:

Step-by-step explanation:

by using  mid -point  formula,

(X1+x2/2),(y1+y2/2)

=( 6+9/2) ,(1+4/2)= (8+p/2),5/2

15/2,5/2=(8+p/2),5/2

15/2=8+p/2

15=8+p

P=7