# Let ABCD is a square whose two vertices A and D lie on positive x-axis and positive y-axis respectively.If the co-ordinate of C is(15,19),then the co-ordinate of B are:1. (19,4)2.(4,19)3.(19,15)4.(19,11)

Jitender Singh IIT Delhi
8 years ago
Ans: (19, 4)
Sol:
Let the coordinates of A, B & D be:
$A(a, 0), B(c, d), D(0, b)$
Equate the sides of the square:
$a^{2}+b^{2}=15^{2}+(19-b)^{2}=(a-c)^{2}+d^{2}=(15-c)^{2}+(19-d)^{2}$Equating diagonals of square:
$(15-a)^{2}+(19)^{2}=c^{2}+(d-b)^{2}$
After solving all the equations, you would find
$a = 4$
$b = 15$
$c = 19$
$d = 4$
Thanks & Regards
Jitender Singh
IIT Delhi