Question

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

Answer 1

Answer:

P = 7

Step-by-step explanation:

Since,

AB = CD. ---(i)

AB = sqrt((8-6)^2 + (2-1)^2)

AB = root5

CD = sqrt((p-9)^2 + (3-4)^2) = root5[by(i)]

sqrt((p)^2 + 82 - 18p) = root5

square both sides =》

p^2 + 82 - 18p = 5

p^2 + 77 - 18p = 0

P^2 - 11p - 7p + 77 = 0

p(p-11) -7(p-11) = 0

(p-11) (p-7) = 0

p = 7 or p = 11

By putting p as 11 we did'nt get the answer.

So, p = 7.

Answer 2

$\huge\star\mathfrak\red{{Hey Mate...!!}}$

We know that

● The diagonals of a parallelogram bisect each other. So, coordinates of the mid-point of diagonal AC are same as the coordinates of the mid-point of diagonal BD.

● For rest of the answer refer to the attachment.