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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Related Questions
Construct triangle ABC, with AB = 7 cm, BC = 8 cm and ∠ABC = 60°. Locate by construction the point P such that :
(i) P is equidistant from B and C and
(ii) P is equidistant from AB and BC.
(iii) Measure and record the length of PB.
Use ruler and compasses only for this question.
(i) Construct △ABC, where AB = 3.5 cm, BC = 6 cm and ∠ABC = 60°.
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and record the length of PB.
Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 105°.
Hence,
(i) Construct the locus of points equidistant from BA and BC.
(ii) Construct the locus of points equidistant from B and C.
(iii) Mark the point which satisfies the above two loci as P. Measure and write the length of PC.
Using ruler and compasses, construct
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(ii) the locus of points equidistant from A and C.