Posted by **Princess Mae Campana** on Tuesday, January 29, 2013 at 9:56pm.

The (x,y) is equidistant from (0,0) and (4,-2). Find its algebraic equation.

- analytic geometry -
**Reiny**, Tuesday, January 29, 2013 at 11:26pm
must be on the right bisector of the line joining (0,0) and 4,-2)

slope of that line is (-2-0)/(4-0) = -1/2

so the slope of the right-bisector must be +2

and we can start by saying the equation of the right-bisector must be

y = 2x + b

but we also know that the mid point of our line segment must lie on this

midpoint = ((4+0)/2 , (-2+0)/2 ) = (2, -1)

so in y = mx + b

-1 = 3(2) + b

b = -7

y = 2x - 7

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