Question:
8. Find the point on y–axis which is equidistant from the point (3, 1, 2) and (5, 5, 2).
Answer:
Let the point on y–axis is O(0, y, 0)
Given points are: A(3, 1, 2) and B(5, 5, 2)
Now, OA = OB
=> OA2 = OB2
=> (3 - 0)2 + (1 - y)2 + (2 - 0)2 = (5 - 0)2 + (5 - y)2 + (2 - 0)2
=> 9 + 1 + y2 - 2y + 4 = 25 + 25 + y2 - 10y + 4
=> 9 + 1 - 2y = 25 + 25 - 10y
=> 10 - 2y = 50 - 10y
=> 10y - 2y = 50 - 10
=> 8y = 40
=> y = 40/8
=> y = 5
So, the point is (0, 5, 0)
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