Write true or false out of the following statements and give the justification of your answer.
(i) The set of points situated at equal distances from a line is a line.
(ii) A circle is the locus of those points which lie at a fixed distance from a given point.
(iii) Three given points will be collinear when they are not the members of the set of points of a line.
(iv) The locus of points equidistant from two lines will be a line parallel to both the lines.
(v) The locus of point equidistant from the given points is the perpendicular bisector of the line joining both the points.
(i) False
The locus of the points situated at equal distances from a line is the lines parallel to the line on its both sides.
(ii) True
(iii) False
Three given points will be collinear only when they belong to the same set of numbers.
(iv) False
It is not always true as if the lines are parallel then it will be a line parallel to them while in case of intersecting lines the line will be the bisector of the angle formed at the point of intersection.
(v) True
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