Question:
find the coordinates of a point on x axis which is equidistant from (2,5) and (-2,9)
Answer:
Let the point on the x-axis is A (x,0).
Let two points are B (2,5) and C (-2,9).
Given that
AB = AC
=> AB2 = AC2
=> (x - 2)2 + 52 = (x+2)2 + 92
=> x2 + 4 - 4x + 25 = x2 + 4 + 4x + 81
=> 29 - 4x = 4x + 85
=> 29-85 = 4x+4x
=> 8x = -56
=> x = -56/8
=> x = -7
So coordinate of a point on x-axis is (-7,0)
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