Posted by **Lance** on Sunday, January 13, 2013 at 5:26am.

A point is equidistant from (-2,4) and (3,5). It is also equidistant from (-2,-3) and (6,-1). Find the point

Please I need Help with this

- Analytic Geometry -
**Reiny**, Sunday, January 13, 2013 at 8:47am
The point must be on the right-bisector of the line segment from (-2,4) to (3,5)

slope of line segment is 1/5, so slope of right-bisector is -5

midpoint of line segment is (1/2 , 9/2)

equation of right-bisector of line segment is

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

2y - 9 = -10x + 5

10x + 2y = 14

5x + y = 7 or y = -5x+7

2nd line segment:

slope of line segment = 2/8 = 1/4

slope of right-bisector = -4

midpoint = (2, -2)

equation of right-bisector

y+2 = -4(x-2)

y +2 = -4x+8

y = -4x + 6

then:

-4x+6 = -5x+7

x = 1

which makes y = -4(1)+6 = 2

the point is (1,2)

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