Please clarify this doubt :

QUESTION :

FIND THE POINT ON THE X AXIS WHICH IS EQUIDISTANT FROM ( 2,-5) AND ( -2, 9 )

DOUBT :

THIS PROBLEM WHEN SOLVED CONSIDERING THE TWO PINTS GIVEN GIVEN AS P AND Q AND THE MID POINT AS R , WE GET PR = QR AND WE GET RESULT AS R = ( -7, 0 )

WHY DOES THE SECTION FORMULA REDUCED TO EQUIDISTANT FORMULA  ( X1 + X2 )/ 2  SINCE M1 = M2  DOES NOT GIVE SAME ANSWER .

SO IS THE EQUIDISTANT FORMULA NOT VALID TO BE USED WHEN THE INTERSECTION IN ON THE AXIS ( X AXIS OR Y AXIS ).

THE SAME EQUIDISTANT FORMULA WORKS IN OTHER CASES, FOR EXAMPLE IN THE BELO W QUSETION ( TRISECTION ).

FIND THE COORDINATES OF THE POINTS OF TRISECTION OF THE LINE SEGMENT JOINING POINTS A( 2,-2), B(-7,4 ).

PLEASE CLARIFY IMMEDIATELY.

THANKS

 

FIND THE POINT ON THE X AXIS WHICH IS EQUIDISTANT FROM ( 2,-5) AND ( -2, 9 )

Solution: 

Let (x ,0) be the point on x-axis which is equidistant from (2, - 5) and (- 2, 9)

therefore, by using distance formula,

Thus, (-7, 0) be the point on x-axis which is equidistant from (2, -5) and (-2, 9).

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