If in a parallelogram ABCD, the coordinates of A,B and C are respectively (1,2),(3,4) and
(2,5), then the equation of the diagonal AD is
Answers
equation of diagonal AD is 5x + 3y - 11 = 0
A parallelogram ABCD is given in which coordinates of A, B , C are (1, 2), (3, 4) and (2, 5) respectively.
we know, midpoints of diagonals of parallelogram meet at a single point.
let point D = (x , y)
i.e., midpoint of diagonal of AD = midpoint of diagonal of BC
⇒{(1 + x)/2, (2 + y)/2} = {(3 + 2)/2, (4 + 5)/2}
⇒{(1 + x)/2, (2 + y)/2} = (5/2, 9/2}
on comparing we get,
(1 + x)/2 = 5/2 ⇒x = 4
(2 + y)/2 = 9/2 ⇒x = 7
so, D = (4, 7)
now equation of AD ;
(y - 2) = (7 - 2)/(1 - 4) (x - 1 )
⇒(y - 2) = 5/-3 (x - 1)
⇒3(y - 2) + 5(x - 1) = 0
⇒3y - 6 + 5x - 5 = 0
⇒5x + 3y - 11 = 0
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