Question

find co-ordinate of D if A(0'0),B(2'0),C(2'2) and D(x,y) forms a square​

Answer 1

Answer:

to form a square the coordinates must be (0,2)

Answer 2

$Given \: A(0,0) , B(2,0), C(2,2) \:and \: D(x,y)$

$forms \: a \: square .$

$\blue{ Diagonals \: bisects \: each \: other }$

$\blue{ in \: a \: square }$

$Mid \:point \: of \: BD = Mid \:point \: of \: AC$

$\implies \Big( \frac{2+x}{2} , \frac{0+y}{2} \Big) = \Big( \frac{0+2}{2} , \frac{0+2}{2} \Big)$

$\implies \Big( \frac{2+x}{2} , \frac{y}{2} \Big) = ( 1 , 1 )$

$\implies \frac{2+x}{2} = 1 \:and \: \frac{y}{2}=1$

$\implies 2 + x = 2 \: and \: y = 2$

$\implies x = 2 - 2\: and \: y = 2$

$\implies x = 0\: and \: y = 2$

Therefore.,

$\red{ D(x,y)} \green { = (0,2)}$

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