Analytic Geometry
posted by Lance .
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

The point must be on the rightbisector of the line segment from (2,4) to (3,5)
slope of line segment is 1/5, so slope of rightbisector is 5
midpoint of line segment is (1/2 , 9/2)
equation of rightbisector 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 rightbisector = 4
midpoint = (2, 2)
equation of rightbisector
y+2 = 4(x2)
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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