math
posted by Coordinate Geometry .
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 !!:)
Respond to this Question
Similar Questions

maths  geometry
In a space with an orthonormal coordinate system consider the plane; &: 4x3y=12 (a)(i)Find the coordinates of the points of intersection of the plane & with the coordinates axes (=axes intersections? 
math
Quadrilateral ABCD is a square. The coordinates of point A are (3,2), coordinates of point B are (3,2),and the coordinates of points C are (3,4). where on a coordinate plane would I mark the location of point D? 
Math
19. Point A(4, 2) is translated according to the rule (x, y) (x + 1, y – 5) and then reflected across the yaxis. a) In which quadrant of the coordinate plane is point A located? 
science
The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system … 
physics
The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system … 
physics
The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system … 
science
The most convenient way to express vectors in the two dimensional plane is in the familiar (x,y) Cartesian coordinates. However, one can express vectors in other coordinate systems as well. For example, another useful coordinate system … 
Math Ms. Sue? Steve? Writeacher?
Point A(4,2) is translated according to the rule (x,y)>(x+1,y5) and then reflected across the y axis a)In which quadrant of the coordinate plane is point A located? 
Math
1. How can you represent a loss of 24 dollars as an integer? 
Math
1. How can you represent a loss of 24 dollars as an integer?