A straight line AB is 8 cm long. Draw and describe the locus of a point which is :

(i) always 4 cm from the line AB.

(ii) equidistant from A and B.

Mark the two points X and Y, which are 4 cm from AB and equidistant from A and B. Describe the figure AXBY.

Steps of construction :

1. Draw a line segment AB = 8 cm.

2. Draw two parallel lines l and m to AB at a distance of 4 cm.

3. Draw CD, the perpendicular bisector of AB which intersects parallel lines l and m at X and Y.

4. Join AX, AY, BX and BY.

Since, diagonals of AXBY are equal and intersect at right angles.

Hence, AXBY is a square.

(i) Hence, locus of point at a distance of 4 cm from AB will be a pair of lines, each parallel to AB.

(ii) Hence, locus of point equidistant from A and B will be perpendicular bisector of AB.