Lesson G2

G2 Ruler and compass constructions and loci Quiz: AQA Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G2, Ruler and compass constructions and loci: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 4: Geometry and measures, written with Revision Ninja.

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The 20 questions

  1. Which construction gives the perpendicular bisector of a line segment AB?

    • Draw a circle centred on the midpoint of AB with radius AB, then join the points where it crosses AB
    • Draw equal arcs from A and B so they cross, then join the crossing point to the midpoint of AB
    • Draw one arc from A and one from B, then join the two points where they meet on one side only
    • Draw equal arcs from A and B so they cross on both sides, then join the two crossing points

  2. What angle is constructed by drawing an equilateral triangle with ruler and compass?

    • 45 degrees
    • 90 degrees
    • 60 degrees
    • 30 degrees

  3. What is the perpendicular distance from a point to a line?

    • The longest distance from the point to the line
    • The shortest distance from the point to the line
    • The distance to the midpoint of the line
    • The distance measured at 45 degrees

  4. What is the locus of points exactly 3 cm from a fixed point?

    • A square of side 3 cm drawn around the fixed point
    • A semicircle of radius 3 cm centred on the fixed point
    • A circle of radius 3 cm centred on the fixed point
    • A straight line 3 cm from the fixed point in every direction

  5. What is the locus of points equidistant from two points A and B?

    • The bisector of the angle AB
    • The perpendicular bisector of AB
    • A circle centred on A
    • The line through A and B

  6. What is the locus of points equidistant from two intersecting lines?

    • A circle centred on the intersection
    • The perpendicular bisector of one line
    • A line parallel to both lines
    • The angle bisector between the two lines

  7. Which construction bisects a given angle?

    • Draw a parallel line through the vertex, then mark equal lengths along each arm
    • Draw one arc from the vertex across both arms, then bisect the arc with a ruler line
    • Draw equal arcs from the vertex across both arms, then equal arcs from those crossing points
    • Draw a line from the vertex to the midpoint of the two arms, then extend it

  8. What is the locus of points that are always 2 cm from a given line?

    • Two lines parallel to the original line, each 2 cm away
    • A single line through the midpoint, at right angles
    • A circle of radius 2 cm centred on the original line
    • A pair of semicircles of radius 2 cm at each end of the line

  9. Which is the correct method to construct an equilateral triangle with side 5 cm?

    • Draw a 5 cm line, then arcs of radius 2.5 cm from each end meeting at the apex
    • Draw a 5 cm line, then arcs of radius 5 cm from each end meeting at the apex
    • Draw two 5 cm lines at a right angle to each other, then join their ends
    • Draw a 5 cm line, bisect it, then join the midpoint to each end

  10. Which set is the locus of points closer to A than to B?

    • The whole line AB extended beyond A in both directions
    • The perpendicular bisector of AB only, with no points on either side
    • The circle centred on A with radius AB, including its inside
    • The side of the perpendicular bisector of AB that contains A

  11. Which tool is used to mark a line segment of an exact length in a construction?

    • A ruler
    • A compass
    • A protractor
    • A set square

  12. Which tool is needed to draw arcs in constructions?

    • A compass
    • A set square
    • A ruler
    • A protractor

  13. What angle is obtained by bisecting a 60 degree angle?

    • 120 degrees
    • 45 degrees
    • 30 degrees
    • 15 degrees

  14. Two points A and B are 6 cm apart. What radius must the arcs have when constructing the perpendicular bisector?

    • Exactly 6 cm
    • Exactly 12 cm
    • Less than 3 cm
    • More than 3 cm

  15. What is the locus of points 4 cm from a line segment of length 6 cm?

    • A circle with diameter 6 cm centred on the segment
    • Two parallel lines 4 cm away, joined by straight ends
    • Two parallel lines 4 cm away plus semicircles at each end
    • A rectangle 4 cm wide, with sides matching the segment

  16. What is the locus of points equidistant from two parallel lines?

    • A single point at the midpoint between the lines
    • One of the two parallel lines, extended to infinity
    • A circle drawn between the two parallel lines
    • A line midway between the two parallel lines

  17. Which tool draws a circle of a given radius?

    • A set square placed at the centre
    • A compass set to the radius
    • A ruler measured to the radius
    • A protractor with the radius marked

  18. Which construction draws a line perpendicular to line l through a point P on l?

    • Mark equal arcs either side of P, then bisect the gap between those two marks
    • Measure 90 degrees with a protractor from P, then draw the line through it
    • Draw an arc from P that cuts l twice, then bisect the segment between those points
    • Draw a parallel line through P using a set square, then extend it past P

  19. Why is the perpendicular bisector construction valid?

    • It is always a diagonal of the segment
    • Every point on it is twice as far from one end as the other
    • It always passes through the origin
    • Every point on it is equidistant from both ends of the segment

  20. Which construction gives a perpendicular from a point P, not on line l, to the line l?

    • Draw an arc from P that touches l once, then join it to the nearest point of l
    • Draw an arc centred on P that cuts l twice, then bisect the segment between those two points
    • Draw a line from P at 45 degrees to l, then measure the length to the line
    • Measure the angle at P with a protractor and draw 90 degrees to meet l

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