math
posted by Coordinate Geometry on .
A(4,7) and B(3,2) are points on a coordinate plane.Find the coordinates of a point C on the xaxis such that AC=BC .

If you make a sketch it should be easy to see that point C must be on the rightbisector of AB
midpoint of AB = ( (43)/2 , (7+2)/2) = (1/2 , 9/2)
slope o AB = (27)/(34) = 5/7
so the slope of the rightbisector is 7/5
equation of rightbisector:
y  9/2 = (7/5)(x  1/2)
for the xintercept, let y = 0
9/2 = (7/5)(x1/2)
9/2 = 7x/5 + 7/10
times 10
45 = 14x + 7
14x = 52
x = 52/14 = 26/7
point C is (26/7, 0)
or
let the point be C(x,0)
AC = BC
√( (x4)^2 + 7^2) = √( (x+3)^2 + 4^2)
square both sides
(x4)^2 + 49 = (x+3)^2 + 4
x^2  8x + 16 + 49 = x^2 + 6x + 9 + 4
14x = 52
x = 52/14 = 26/7 , just like before 
THANKS A LOT !!:)