Femi's corner shop offers free delivery to any address within 6 cm of the shop, marked \(C\) on his plan below. A regular customer's address is marked \(X\)...
Question 1 Report
Femi's corner shop offers free delivery to any address within 6 cm of the shop, marked \(C\) on his plan below. A regular customer's address is marked \(X\).
- Using compasses only, construct the locus of points that are exactly 6 cm from \(C\). (2)
- State, giving a reason, whether \(X\) qualifies for free delivery. (1)
Answer Details
The set of all points a fixed distance from a single point \(C\) is, by definition, a circle centred on \(C\) with that distance as its radius.
(a) Using compasses only, set the radius to \(6\) cm (measured against the given scale) and, with the point fixed on \(C\), draw a complete circle. [1 mark] The circle must be drawn accurately, with the compass setting undisturbed all the way around, since any slip changes the radius partway through the circle. [1 mark]
(b) \(X\) qualifies for free delivery. Reading \(X\)'s position relative to \(C\) as \(4\) across and \(2\) up, the distance is \(CX = \sqrt{4^2 + 2^2} = \sqrt{20} \approx 4.5\) cm by Pythagoras' theorem, and \(4.5\) cm is less than the \(6\) cm delivery radius, so \(X\) lies inside the circle of free delivery. [1 mark]
Exam tip: to decide whether a point lies inside a locus circle, always compare the calculated distance with the radius directly, rather than trying to judge it from a sketch; a distance smaller than the radius means the point is inside.
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