Grace is budgeting for a new smoke alarm, which covers rooms up to 3.5 cm from its position on the floor plan below, and two internal walls meet at a marked...
Question 1 Report
Grace is budgeting for a new smoke alarm, which covers rooms up to 3.5 cm from its position on the floor plan below, and two internal walls meet at a marked corner.
- Construct the locus of points 3.5 cm from the alarm. (2)
- Construct the bisector of the marked wall angle. (2)
Answer Details
This question needs a fixed-distance locus (a circle) and an angle bisector (equidistance from two walls).
(a) The locus of points within \(3.5\) cm of the alarm is a circle of radius \(3.5\) cm centred on the alarm's marked position; draw it with compasses, keeping the radius undisturbed throughout, so every point on the circle is exactly \(3.5\) cm from the centre. [2 marks]
(b) For the wall angle, draw an arc from its vertex crossing both walls, then draw equal-radius arcs from those two crossing points so they intersect inside the angle; a line from the vertex through that intersection bisects the angle, since it is equally spaced from both walls. [2 marks]
Both constructions completed on the floor plan:
Exam tip: "covers rooms up to a distance" is the language of a circular locus around a single point, while "meet at a corner" and being asked to bisect it is the language of an angle bisector; matching the wording to the construction avoids confusing the two.
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