ECZ 2021 · O-Level Paper 2 · Question 6 — Construction and Loci

Question from ECZ 2021 · O-Level Paper 2 · Question 6

(a(i)) Construct triangle ABC in which AB = 6 cm, BC = 9 cm and AC = 5 cm.[1]

Verified working — step 1

Draw BC = 9 cm (the longest side first).

(a(ii)) Measure and write the size of angle ABC.[1]

Verified working — step 1

All three sides known, so cosine rule for the angle:

(b) Within the triangle ABC, draw the locus of points which are

(b(i)) equidistant from A and C,[1]

Verified working — step 1

Points equidistant from A and C lie …

(b(ii)) 3 cm from A,[1]

Verified working — step 1

The locus 3 cm from the point A is a…

(b(iii)) equidistant from AC and BC.[2]

Verified working — step 1

AC and BC meet at C, so points equidistant …

(c) A point P, within triangle ABC, is such that it is less than or equal to 3 cm from A, nearer to BC than AC and closer to A than to C. Indicate clearly by shading, the region in which P must lie.[2]

Verified working — step 1

At most 3 cm from A: inside the arc from (b)(ii).

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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