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Question
Draw and describe the locus in the following case:
The locus of a point in rhombus ABCD which is equidistant from AB and AD.
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Solution
The locus of a point in the rhombus which is equidistant from AB and AD is the diagonal AC.
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Ruler and compasses 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 a ΔABC, in which BC = 6 cm, AB = 9 cm and ∠ABC = 60°.
(ii) Construct the locus of the vertices of the triangles with BC as base, which are equal in area to ΔABC.
(iii) Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
(iv) Measure and record the length of CQ.
