# Thread: equations of line and plane

1. ## equations of line and plane

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

can someone show me how this is done?
what is equidistant..?
thanks for any help

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

can someone show me how this is done?
what is equidistant..?
thanks for any help
equidistant means of equal distance. so all point equidistant from (-4,2,1) and (2,-4,3) are those points which are of equal distance between (-4,2,1) and (2,-4,3). that is, if we call such a point (x,y,z), then at any time, the distance between (x,y,z) and (-4,2,1) is the same as the distance between (x,y,z) and (2,-4,3). that should give you a hint on how to solve the problem. use the distance formula. find the formula that gives the shortest distance between (x,y,z) and (-4,2,1) and then find the formula that gives the distance between (x,y,z) and (2,-4,3). then equate them and solve.

3. Originally Posted by xfyz
Find an equation for the plane consisting of all points that are equidistant from the points (-4,2,1) and (2,-4,3)
The set of points equidistance from two points is a plane that contains the midpoint of the segment and has its normal parallel to the vector determined by the points.

The midpoint of the line segment determined by those points is (-1,-1,2).
The vector determined is <6,-6,2>.
Use the vector <3,-3,1> as the normal to write the equation of the plane containing (-1,-1,2).