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

Why can't we use midpoint formula? 

Since it lies in between them

Asked by Acharyaarjun410 | 22nd Apr, 2020, 10:02: AM

Expert Answer:

Let A be the point which is equidistant from B(2, -5) and C(-2, 9)
The coordinates of A will be (a, 0) as it lies on the x-axis
Therefore BA = AC
rightwards double arrow square root of open parentheses 2 minus a close parentheses squared plus open parentheses negative 5 minus 0 close parentheses squared end root equals square root of open parentheses negative 2 minus a close parentheses squared plus open parentheses 9 minus 0 close parentheses squared end root
rightwards double arrow open parentheses 2 minus a close parentheses squared plus 25 equals open parentheses negative 2 minus a close parentheses squared plus 81
rightwards double arrow 4 plus a squared minus 4 a plus 25 equals 4 plus a squared plus 4 a plus 81
rightwards double arrow 29 minus 4 a equals 4 a plus 85
rightwards double arrow negative 56 equals equals 8 a
rightwards double arrow a equals negative 7
Note:- The midpoint formula can't be used because it is not necessary that the mid-point lies on the axis.

Answered by Renu Varma | 22nd Apr, 2020, 10:20: AM