AB is a line - segment. P and Q are points on either side of AB such that each of them is equidistant from the points A and B. Show that the line PQ is the perpendicular bisector of AB.

AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B.

In the isosceles DeltaABC , AB = AC , O is any point on the side BC. OP and OQ are the perpendicular distance of the sides AB and AC from O respectively. BD is the perpendicular distance of AC from B. Show that OP + OQ = BD.

Draw the perpendicular bisector of a given line segment AB=7cm.

Draw the perpendicular bisector of a given line segment AB=6cm.

Draw the perpendicular bisector of a given line segment AB=8cm.

P is a point equidistant from two lines l and m intersecting at point A (see figure). Show that the line AP bisects the angle between them.

Find the equation to the perpendicular bisector of the line -segment joining the two points (2,3) and (4,-1). What is the length of the perpendicular drawn from the origin to that perpendicular bisector ?

P and Q are such two points on the line segment obtained by joining the points A (-2, 5) and B (3, 1) that AP = PQ = QB. Then find the coordinates of the mid-point of PQ.

Let AB be a line segment of length 4 unit with the point A on the line y=2x and B on the line y=x. Then locus of middle point of all such line segment is

In a right triangle ABC right-angled at B, if P and Q are points on the side AB and AC respectively, then___