Question

if the points A(6,1 ),B(8,2)C(9,4)and D(p,3) are the vertices of a parallelogram , find the value of p​

Answer 1

The value of p is 7

      1.  The given points of the parallelogram are

         A(6,1);B(8,2);C(9,4);D(p,3)

      2.  we know that,

                  Diagonals of the parallelogram bisects each other

      3. midpoint of AC=midpoint of BD

                     MIDPOINT=$(\frac{A+B}{2} )$

       4.Therefore,

                   $(\frac{6+9}{2}+\frac{1+4}{2} ) =(\frac{8+p}{2}+\frac{2+3}{2} )$

                           $(\frac{15}{2},\frac{5}{2} )=(\frac{8+p}{2},\frac{5}{2} )$

        5.Equating the x and y cordinates

         6.Then

               15/2  =    8+p/2

                   15 = 8+p

                     p = 7

Answer 2

Answer:

7

Step-by-step explanation:

given points A(6,1),B(8,2),C(9,4),D(p,3) are the vertices of a parallelogram.

from the question we need to find p?

we know that " A quadrilateral is said to be a parallelogram if a pair of opposite sides are equal and parallel ".

so from the condition ....the opposite sides of the parallelogram should be equal

i.e, AB=CD

that means,the distance between the points A and B must be equal to the distance between C and D

therefore the distance between the two points (x1,y1) and (x2,y2) is given by sqrt((x2-x1)²+(y2-y1)²);

that implies

sqrt((8-6)²+(2-1)²)=sqrt((p-9)²+(3-4)²)

(2)²+(1)² = (p-9)²+(-1)²

4+1 = (p-9)²+1

4 = (p-9)²

therefore p-9= -2

p= 9-2

p= 7

therefore the values of p is 7