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What is the locus of points equidistant from the points a...
by diana
what is the locus of points equidistant from the points A(2,5) and B(4,5)?
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Locus of points equidistant from two points, is perpendicular bisector of line determined by two points.

Given: A=(2,5) and B=(4,5)
Let (x, y) be a point on perpendicular bisector.

Distance b/w (x,y) and (2,5)= sqrt[(x-2)2+(y-5)2]
And b/w (x,y) and (4,5)= sqrt[(x-4)2+(y-5)2]

Equating and squaring both distances
(x-2)2+(y-5)2=(x-4)2+(y-5)2
x2-4x+4+y2-10y+25=x2-8x+16+y2-10y+25
By canceling and collecting terms
4x-12=0
x-3=0

This is required equation. All points on it will be equidistant from A and B.

Related video links: Distance Formula
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by Winpossible
May 06, 10 12:36AM PST
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