equation of a plane between two points

[acpodgorski]

Find an equation for the plane consisting of all points that are equidistant from the points (-4,2,1) and (2,-4,3).

i found the midpoint which i knew would be a point on the plane between these which came to be (-1,-1,2). what do i do from here?

 

[royhaas]

You are correct, but you're not answering the question. Find the equations for the (squared) distance between (x,y,z) and each of your end points. Set the equations equal to each other, then do the algebra. The quadratic terms all cancel, leaving you with an equation for the plane.

 

[Deleted member 4993]

The line joining these two points will be normal to the plane in question.

What is the relationship between the equation of a normal and the equation of the plane?

 

[acpodgorski]

thanks, got it i think, i found the normal between the midpoint(point on the plane) and one of the points on the plane and plugged that in with the point on the plane into the equation of a plane.