Question

Abcd is a square where a (0,0) b (2,0), d (0,2), then find the co

Answer 1

The coordinates of c is c(2,2)
In a square diagonals by sect each other.
Mid point of AC= Mid of BD
Let the coordinates of c(a, b)
(0+a/2,0+b/2)=(2+0/2,0+2/2)=(1,1)
(a, b) =(2,2)

Answer 2

The coordinates of C are (2, 2)

• Given,

             A(0, 0) B(2, 0) D(0, 2)

• Let C = (x, y)
• In a square, all sides are equal.

               $BC =CD\\BC^{2} = CD^{2} \\ (x-2)^{2} + (y-0)^{2} = (x-0)^{2}+(y-2)^{2} \\x^{2} + 4 - 4x + y^{2} = x^{2} + y^{2}+4-4y\\4x - 4y = 0\\x-y=0\\x=y-------(1)$

Similarly,

        $AB = BC\\AB^{2} = BC^{2} \\ (0-2)^{2} + (0-0)^{2}= (x-0)^{2} + (y-2)^{2} \\4=x^{2} +y^{2} +4-4y\\2x^{2} -4x=0 [from (1)]\\2x(x-2)=0\\x-2=0\\x=2\\y=2$

Therefore, the coordinates of C are (2, 2)