Mathematics
A line segment AB is 8 cm long. Locate by construction the locus of a point which is :
(i) Equidistant from A and B.
(ii) Always 4 cm from the line AB.
(iii) Mark two points X and Y, which are 4 cm from AB and equidistant from A and B. Name the figure AXBY.
Locus
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Answer
The figure is shown below:
(i) The locus of a point equidistant from A and B will be perpendicular bisector of AB.
(ii) Let the perpendicular bisector bisect AB at O. Cut an arc of 4 cm from O on CD (perpendicular bisector) on both sides. Mark these points as X and Y.
Hence, locus will be point on perpendicular bisector of AB at a distance of 4 cm on both sides.
(iii) Joining the points A, B, X and Y.
Hence, the figure formed ABXY is a square.
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