Posted by **Coordinate Geometry** on Saturday, March 30, 2013 at 7:22am.

A(4,7) and B(-3,2) are points on a coordinate plane.Find the coordinates of a point C on the x-axis such that AC=BC .

- math -
**Reiny**, Saturday, March 30, 2013 at 7:40am
If you make a sketch it should be easy to see that point C must be on the right-bisector of AB

midpoint of AB = ( (4-3)/2 , (7+2)/2) = (1/2 , 9/2)

slope o AB = (2-7)/(-3-4) = 5/7

so the slope of the right-bisector is -7/5

equation of right-bisector:

y - 9/2 = (-7/5)(x - 1/2)

for the x-intercept, let y = 0

-9/2 = (-7/5)(x-1/2)

-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

√( (x-4)^2 + 7^2) = √( (x+3)^2 + 4^2)

square both sides

(x-4)^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

- math -
**Anonymous**, Saturday, March 30, 2013 at 11:28am
THANKS A LOT !!:)

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