Prove that the locus of the point equidistant from two given points is the straight line which bisects the line segment joining the given points at right angles.

The locus of the point equidistant from two given points a and b is given by

The locus of a point equidistant from two intersecting lines is

The locus of a point equidistant from three collinear points is

Statement-1: The locus of point z satisfying |(3z+i)/(2z+3+4i)|=3/2 is a straight line. Statement-2 : The locus of a point equidistant from two fixed points is a straight line representing the perpendicular bisector of the segment joining the given points.

Statement - 1 : If the perpendicular bisector of the line segment joining points A (a,3) and B( 1,4) has y-intercept -4 , then a = pm 4 . Statement- 2 : Locus of a point equidistant from two given points is the perpendicular bisector of the line joining the given points .

Find the equation of the plane which bisects the line segment joining the points A(2,3,4) and B(4,5,8) at right angles.

Find the equation of the plane which bisects the line segment joining the points (-1, 2, 3) and (3, -5, 6) at right angles.

The equation of the line bisecting the line segment joining the points (a,b) and (a',b') at right angle,is