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Question

Which point on y-axis is equidistant from (2, 3) and (-4, 1) ?

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Solution

Let the point on y-axis be A(0,y)
It is equidistant from B(2,3) and C(-4,1)
AB= square root of 2 squared plus left parenthesis 3 minus y right parenthesis squared end root
AC=square root of left parenthesis negative 4 right parenthesis squared plus left parenthesis 1 minus y right parenthesis squared end root
AB=AC
square root of 2 squared plus left parenthesis 3 minus y right parenthesis squared end root = square root of left parenthesis negative 4 right parenthesis squared plus left parenthesis 1 minus y right parenthesis squared end root
4 plus 9 plus y squared minus 6 y space equals space 16 plus 1 plus y squared minus 2 y 4 y space equals space minus 4 y space equals space minus 1
Hence the point is (0,-1)

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