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Question
Without using set squares or a protractor, construct:
- Triangle ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm.
- Draw the locus of a point which moves so that it is always 2.5 cm from B.
- Draw the locus of a point which moves so that it is equidistant from the sides BC and CA.
- Mark the point of intersection of the loci with the letter P and measure PC.
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Solution
- Draw a triangle by given measurements.
- The locus of a point which moves so that it is always 2.5 cm from B is a circle, as shown in the figure.
- The locus of a point is the bisector of ∠ACB.
- The circle and bisector intersect in two points PD = 0·9 cm and PC = 3.4 cm.
RELATED QUESTIONS
On a graph paper, draw the lines x = 3 and y = –5. Now, on the same graph paper, draw the locus of the point which is equidistant from the given lines.
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Ruler and compasses may be used in this question. All construction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment.
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- Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
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Draw and describe the lorus in the following cases:
The locus of points at a distance of 4 cm from a fixed line.
Construct a Δ ABC, with AB = 6 cm, AC = BC = 9 cm; find a point 4 cm from A and equidistant from B and C.
How will you find a point equidistant from three given points A, B, C which are not in the same straight line?
Ruler and compass only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.
(i) Construct Δ ABC, in which BC = 8 cm, AB = 5 cm, ∠ ABC = 60°.
(ii) Construct the locus of point 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 as P, the point which is equidistant from AB, BC and also equidistant from B and C.
(v) Measure and record the length of PB.
