Constructions & loci
AQA GCSE Maths revision on Constructions & loci. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
When constructing an angle bisector using a compass and ruler, why must the compass width remain unchanged between the two arcs drawn from the intersection points?
- A) To ensure the arcs are equidistant from the original vertex
- B) To prevent the compass from slipping on the paper
- C) To make the construction lines look symmetrical
- D) To ensure the arcs are large enough to be seen
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Answer: To ensure the arcs are equidistant from the original vertex
The construction of an angle bisector relies on creating a rhombus or kite shape where the diagonals bisect the angles. By keeping the compass width consistent, you ensure that the two points where the arcs intersect are equidistant from the vertex, creating the necessary geometric symmetry to divide the angle exactly in half.
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Question 2
A student is asked to find the locus of points equidistant from two fixed points, A and B. What is the geometric name for this locus?
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Answer: Perpendicular bisector
Any point on the perpendicular bisector of a line segment AB is equidistant from point A and point B. If you pick any point on this line, the distance to A will always equal the distance to B, forming two congruent right-angled triangles.
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Question 3
When constructing a perpendicular from a point to a line, why is it necessary to draw an arc that intersects the line at two separate points?
- A) To create two fixed points that define the perpendicular line
- B) To ensure the arc is perfectly circular
- C) To allow the compass to be reset to a smaller width
- D) To avoid crossing the original line more than once
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Answer: To create two fixed points that define the perpendicular line
By creating two points on the line that are equidistant from the target point, you turn the problem into finding the perpendicular bisector of that new segment. This ensures the resulting line passes through the original point at exactly 90 degrees.
Want to test yourself on the remaining cards for this topic?
13 more questions on Constructions & loci — plus mistakes tracking and spaced repetition across the whole Maths spec.