posted by Stephanies .
Find the equation of the plane for which each point is equidistant from P(2,1,1) and Q (-4,7,9).
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Distance between two points in space,
D = √((x1-x0)²+(y1-y0)²+(z1-z0)²)
Equate the distance between any point in the required plane, (x,y,z) and P(xp,yp,zp) to that between (x,y,z) and Q(xq,yq,zq) to get:
(x-xp)²+(y-yp)²+(z-zp)² = (x-xq)²+(y-yq)²+(z-zq)²
2x(xp-xq)+2y(yp-yq)+2z(zp-zq) - (xp²-xq²+yp²-yq²+zp²-zq²) = 0
Check my algebra.