The sports day committee is marking a triangular flag zone on the field and has already drawn the first boundary edge \(XY\), pictured below. XY© EAGLE BEAC...
Question 1 Report
The sports day committee is marking a triangular flag zone on the field and has already drawn the first boundary edge \(XY\), pictured below.
Construct, using only compasses and a straight edge, triangle \(XYZ\) with sides \(XY = 5\) cm, \(YZ = 9\) cm and \(ZX = 12\) cm. Leave in your construction lines. (3)
Answer Details
With edge \(XY = 5\) cm already marked, the third vertex \(Z\) is fixed by two arcs, one measuring its distance from \(X\) and one measuring its distance from \(Y\).
Open the compasses to \(12\) cm (the length \(ZX\)) and draw an arc centred on \(X\); then open the compasses to \(9\) cm (the length \(YZ\)) and draw an arc centred on \(Y\), so the arcs intersect. [1 mark]
Each radius must be set carefully against the ruler and the compasses kept undisturbed while drawing, since a shifted setting moves the crossing point and makes \(Z\) inaccurate. [1 mark]
The arcs cross at the point that is \(12\) cm from \(X\) and \(9\) cm from \(Y\) at once: that is \(Z\). Triangle \(XYZ\) is completed with straight lines from \(X\) to \(Z\) and \(Y\) to \(Z\), leaving all construction arcs visible. [1 mark]
Exam tip: check that \(5 + 9 > 12\) (the triangle inequality) before starting; here \(14 > 12\), so the triangle is possible and the arcs will meet as expected.
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