Mathematics
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.
Answer
Steps of construction :
Draw a line segment AB = 8 cm.
Draw two parallel lines l and m to AB at a distance of 4 cm.
Draw CD, the perpendicular bisector of AB which intersects parallel lines l and m at X and Y.
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.
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