Question

find the point on the x axis which is equidistant from (2,-5)and(-2,9)

Answer 1

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

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COORDINATE GEOMETRY PROBLEM SOLVING !

As we know that a point on x-axis is of the form ( x , 0 ).

So, let P( x , 0 ) be the point which is equidistant from A  ( 2, -5 ) and B ( -2 ,9 ).

PA = PB

√(x-2)² + ( 0+5 )² = √(x+2)² + (0-9)²

(x-2)² + 25 = (x+2)² + 81

x² - 4x + 4 + 25 = x² + 4x + 4 + 81

-8x = 56

x = -7

$\implies\boxed{\mathsf{Hence\:the\:required\:point\:is\:(-7,0).}}$

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Answer 2

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