The coordinates of two points are A(-2,6) & B(9,3). Find the coordinates of the point C on the X-axis such that AC=BC.

A(-2,6) B (9,3)

We need to
find C on x-axis ==> C (x,0)

such that
:

AC = BC

AC= sqrt(0-6)^2 +
(x+2)^2]= sqrt[(36 + (x+2)^2]

BC= sqrt[(0-3)^2+ (x-9)^2]=
sqrt[(9 + (x-9)^2]

==> AC =
BC

==> sqrt(36+(x+2)^2]= sqrt[(9+
(x-9)^2]

square both
sides:

==> 36 + (x+2)^2 = 9 +
(x-9)^2

==> 36 + x^2 +4x + 4 = 9 + x^2 -18x +
81

Now group
similars:

==> 22x -50 =
0

==> x= 50/22=
25/11

Then the point C is (25/11,
0)