ECZ 2018 · O-Level Paper 2 · Question 4 — Construction and Loci

Question from ECZ 2018 · O-Level Paper 2 · Question 4

(a(i)) Construct a triangle XYZ in which XY = 9 cm, YZ = 7 cm and angle XYZ = 38 degrees.[1]

Verified working — step 1

Draw XY = 9 cm, construct an angle of 38 degrees at Y, mark YZ = …

(a(ii)) Measure and write the length of XZ.[1]

Verified working — step 1

By the cosine rule XZ2 = 92 + 72 - 2(9)(7) cos 38

(b(i)) On your diagram, within triangle XYZ, construct the locus of points which are 6 cm from Y.[1]

Verified working — step 1

Set compasses to 6 cm with centre Y …

(b(ii)) On your diagram, within triangle XYZ, construct the locus of points which are equidistant from XZ and XY.[2]

Verified working — step 1

Points equidistant from two intersecting lines lie on the b…

(c) Mark clearly with the letter P, within triangle XYZ, a point which is 6 cm from Y and equidistant from XZ and XY.[1]

Verified working — step 1

P satisfies both loci, so it lies w…

(d) A point T, within triangle XYZ, is such that its distance from Y is less than or equal to 6 cm and it is nearer to XZ than XY. Indicate clearly, by shading, the region in which T must lie.[2]

Verified working — step 1

At most 6 cm from Y: inside the arc from (b)(i).

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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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