Question

If the points A (6,1) B(8, 2)
c (9,4) and D (P, 3) are
vertices of a parallelogram, taken
in order Find the value of p
C (9,4)
D (P,3)
A (6, 1)
B (8,2)​

Answer 1

★Given:-

• The points A (6,1) B(8, 2)  C(9,4) and D (P, 3) are  vertices of a parallelogram, taken  in order.

★To find:-

• Value of p.

★Solution:-

✦Diagonals of a parallelogram bisect each other.

Hence,coordinates of the mid-point of diagonal AC are same as the coordinates of the mid-point of diagonal BD.

Using the mid-point formula,

✦(x,y) = [(x₁+x₂)/2, (y₁+y₂)/2]

Where,

• (x,y) = coordinates of the midpoint
• (x₁, y₁)=coordinates of the first point
• (x₂, y₂)=coordinates of the second point

Midpoint of AC:-

→(x,y) = [(x₁+x₂)/2, (y₁+y₂)/2]

→(6+9)/2 , (1+4)/2

→15/2 , 5/2

Midpoint of BD:-

→(x,y) = [(x₁+x₂)/2, (y₁+y₂)/2]

→(8+p)/2 , (2+3)/2

→(8+p)/2 , 5/2

We have the condition:

Coordinates of the mid-point of diagonal AC are same as the coordinates of the mid-point of diagonal BD.

Therefore,

→(8+p)/2 , 5/2  = 15/2 , 5/2

→(8+p)/2 = 15/2

→8+p = 15

→p = 15 - 8

→p = 7

Therefore,the value of p is 7.

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