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Grade: 12th pass
The opposite angular points of square are(3,4) and (-1,1) .find the cordinates of the other two verticles .
Plzz solve it briefly
9 months ago

Answers : (1)

Aditya Gupta
2014 Points
let A= (3,4) and B= (-1,1).
now, these are given to be opposite points, which means that they are not adjacent, and lie across the diagonal.
since the diagonals of a square bisect each other and also perpendicular to each other, hence we first write the equation of through the mid point O of A and B perpendicular to diagonal AB.
O= ((3 – 1)/2, (4+1)/2)= (1, 5/2)
slope of AB= (4 – 1)/(3+1)= ¾. so slope of other diag= – 4/3 
so eqn of other diagonal is 3(y – 5/2)= – 4(x – 1).....(1)
so we know that the other vertices lie on the above line. now we also know that angle between the edges is 90 deg. so m1*m2= – 1
or [(y – 4)/(x – 3)]*[(y – 1)/(x+1)]= – 1......(2)
solving (1) and (2), we get
(x, y)= (5/2, 1/2) or (–1/2, 9/2)
and these are precisely the reqd vertices!
kindly approve :)
9 months ago
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