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Loci (Locus and Its Constructions) — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsLoci (Locus and Its Constructions)4 Marks
Question
Use graph paper for this question. Take 2 cm = 1 unit on both the axis.
(i) Plot the points A(1,1), B(5,3) and C(2,7).
(ii) Construct the locus of points equidistant from A and B.
(iii) Construct the locus of points equidistant from AB and AC.
(iv) locate the point P such that PA = PB and P is equidistant from AB and AC.
(v) Measure and record the length PA in cm.
✓

Answer


Steps of Construction:
i) Plot the points A(1,1), B(5,3) and C(2,7) on the graph and join AB, BC and CA.
ii) Draw the perpendicular bisector of AB and angle bisector of angle A which intersect each other at P.
P is the required point.
Since P lies on the perpendicular bisector of AB.
Therefore, P is equidistant from A and B.
Again,
Since P lies on the angle bisector of angle A.
Therefore, P is equidistant from AB and AC.
On measuring, the length of PA = 5.2 cm.

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