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. Solution Let the point C be at (x,y). AC--> D^2 = (-2 - x)^2 + (6 - y)^2 = x^2 + 4x + 4 + y^2 - 12y + 36 BC--> D^2 = (x - 9)^2 + (y - 3)^2 = x^2 - 18x + 81 + y^2 - 6y + 9 AC = BC x^2 + 4x + 4 + y^2 - 12y + 36 = x^2 - 18x + 81 + y^2 - 6y + 9 11x - 25 - 3y = 0 The point C lies on this line. On the x-axis, y= 0. Therefore: 11x - 25 = 0 x = 25/11.

1. 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.
Solution
Let the point C be at (x,y).
AC--> D^2 = (-2 - x)^2 + (6 - y)^2 = x^2 + 4x + 4 + y^2 - 12y + 36
BC--> D^2 = (x - 9)^2 + (y - 3)^2 = x^2 - 18x + 81 + y^2 - 6y + 9
AC = BC
x^2 + 4x + 4 + y^2 - 12y + 36 = x^2 - 18x + 81 + y^2 - 6y + 9
11x - 25 - 3y = 0
The point C lies on this line.
On the x-axis, y= 0. Therefore:
11x - 25 = 0
x = 25/11