# What will be the equation of the locus which is at the same distance from (3,7) and (-2,4).

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by Ark01

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by Ark01

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Find middle point P of the two given points : [ (3-2)/2 , (7+4)/2 ]

= ( 0.5 , 5.5 )

The locus passes through this. The locus is a straight line bisecting perpendicularly the line joining the given points. So find slope of the line joining given points.

slope = (7- 4) / (3 +2 ) = 3/5 = 0.6

Now the perpendicular bisector has as slope of - 1/0.6

So equation of the locus desired :

(y - y1) = m (x - x1)

y - 5.5 = - (x -0.5) / 0.6

0.6 y - 5.5*6 = - x + 0.5

** 0.6 y + x = 3.8 or 3 y + 5 x = 19**

= ( 0.5 , 5.5 )

The locus passes through this. The locus is a straight line bisecting perpendicularly the line joining the given points. So find slope of the line joining given points.

slope = (7- 4) / (3 +2 ) = 3/5 = 0.6

Now the perpendicular bisector has as slope of - 1/0.6

So equation of the locus desired :

(y - y1) = m (x - x1)

y - 5.5 = - (x -0.5) / 0.6

0.6 y - 5.5*6 = - x + 0.5