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Answer:
(2,2)
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Answered by
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Answer:
Coordinates are C(2,2)
Step-by-step explanation:
By using distance formula, we have:
AB = √[( x2 - x1)^2 + (y2 - y1)^2]
=> AB = √[( 2)^2 + (0)^2]
=> AB = √4
=> AB = 2 units
Now, All sides of a square are equal and let coordinates of C be C( x, y)
=> AB = BC
=> BC = 2 units
2 = √[( x - 2)^2 + ( y - 0)^2]
=> 2 = √[ x^2 + 4 - 4x + y^2]
CD = 2
=> 2 = √[( x - 0)^2 + ( y - 2)^2]
=> 2 = √[ x^2 + y^2 + 4 - 4y]
=> √[ x^2 + y^2 + 4 - 4y] = √[ x^2 + 4 - 4x + y^2]
=> x^2 + y^2 + 4 - 4y = x^2 + 4 - 4x + y^2
=> 4x = 4y
=> x = y. --------------------(1)
BD = √[ ( 2 - 0)^2 + ( 0-2)^2]
= √8 units
AC = BD. ( diagnols of a square are equal)
=> √8 = √[( x - 0)^2 + (y - 0)^2]
=> 8 = x ^2 + y^2
But from (1) , x = y
=> 8 = x^2 + x^2
=> x^2 = 4
=> x = 2 .
since x = y, y = 2
Therefore, coordinates of point C are C( 2,2)
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