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Find the point in XY-plane which is equidistant from three points A(2,0,3), B(0,3,2) and C(0,0,1)

Find the point in XY-plane which is equidistant from three points A(2,0,3), B(0,3,2) and C(0,0,1)

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1 Answers

Latika Leekha
askIITians Faculty 165 Points
7 years ago
Hello student,
Since we are required to find out the point in the xy-plane, hence the z-coordinate would be zero.
Let the required point be P(x, y, 0).
Then AP = BP = CP (Since it is equidistant from A, B and C.
Hence, AP2 = BP2 = CP2
AP2 = CP2
This means, (x-2)2 + (y-0)2 + (0-3)2 = (x-0)2 + (y-0)2 + (0-1)2
x2 + 4 – 4x + y2 + 9 = x2 + y2 + 1
We get x = 3.
BP2 = CP2
This means, (x-0)2 + (y-3)2 + (0-2)2 = (x-0)2 + (y-0)2 + (0-1)2
x2 + y2 + 9 – 6y + 4 = x2 + y2 + 1
We get y = 2.
Hence, the required point is P(3,2 ,0).

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