Printable · GCSE Foundation · ages 14-16

Ruler and compass constructions and loci worksheet — GCSE Foundation

Fifteen questions on "ruler and compass constructions and loci" — DfE statement G2. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

Non-calculator

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Ruler and compass constructions and loci worksheet — GCSE Foundation

Maths · GCSE Foundation · G2 · Ruler and compass constructions and loci · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A perpendicular bisector is drawn through the midpoint of a line segment AB. Which set of points does this construction show?
(a)the single point exactly halfway along AB
(b)points as far from A as the length AB
(c)points twice as far from A as from B
(d)points the same distance from A as from B
2.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?
(a)Draw equal arcs from X and Y, meeting below line l.
(b)Draw an arc centred at P through only one of X or Y.
(c)Join X and Y with a straight line.
(d)Draw a circle through X, Y and P.
3.Two straight lines cross at a point. To find the points that are the same distance from both lines, which construction should be used?
(a)construct a perpendicular from the crossing point
(b)bisect the angle between the two lines
(c)construct the perpendicular bisector of the two lines
(d)draw a circle centred at the crossing point
4.A ship's radio can be heard up to 30 km from the ship. A lighthouse's light can be seen up to 20 km from the lighthouse. The ship and the lighthouse are 40 km apart along the coast. Describe the region where BOTH the radio can be heard AND the light can be seen.
(a)the lens-shaped region where the two circles overlap
(b)the whole smaller circle, since it fits inside the larger one
(c)no overlap — 30 km and 20 km don't add to 40 km
(d)a straight strip, exactly halfway between the two
5.A construction for the perpendicular bisector of AB begins by opening a pair of compasses to more than half the length of AB, then drawing an arc centred at A. What is the next step?
(a)an arc of the same radius, centred at the midpoint of AB
(b)an arc of the same radius, centred at B
(c)a smaller arc, centred at A again
(d)a straight line joining the ends of the first arc
6.A dog is tied by a lead 4 m long to a fixed ring on a straight garden wall. The wall extends much further than the lead can reach in both directions, and the dog cannot cross through it. Describe the region the dog can reach.
(a)A rectangle 4 m wide, running along the wall.
(b)A semicircle of radius 4 m, away from the wall.
(c)A full circle of radius 4 m.
(d)A quarter circle of radius 4 m.
7.Compasses are opened to exactly half the length of AB, and arcs are drawn centred at A and at B, to construct the perpendicular bisector of AB. Why does this fail?
(a)The radius must equal the full length of AB.
(b)The arcs only meet exactly on AB, not above or below it.
(c)That radius is always too short to draw any arc.
(d)The arcs would not cross the line AB at all.
8.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?
(a)4
(b)0
(c)2
(d)1
9.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?
(a)Join the two crossing points with a straight line.
(b)Draw wider arcs from each crossing point, meeting above.
(c)Draw an arc centred at P through only one crossing point.
(d)Draw a circle centred at P through both crossing points.
10.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.
(a)a line parallel to both, 3 cm from each
(b)the perpendicular bisector of the gap
(c)a line parallel to both, 6 cm from each
(d)a circle of radius 3 cm, centred midway
11.A gardener wants to plant a tree so that it is the same distance from two straight garden walls that meet at a corner, and also the same distance from two ornamental posts standing 4 m apart. Which construction locates this point?
(a)where the angle bisector meets the posts' perpendicular bisector
(b)where the angle bisector meets the line joining the posts
(c)the perpendicular bisector of the posts, alone
(d)the angle bisector of the corner, alone
12.Triangle ABC is drawn. The interior angle bisectors from vertices A and B are constructed and meet at point I inside the triangle. Which statement about point I must be true?
(a)I is the midpoint of side AB.
(b)I lies on side AC.
(c)I is the same distance from all three sides.
(d)I is the same distance from all three vertices.
13.A locus is described as the set of points exactly 4 cm from a fixed point O. What shape is this locus?
(a)a circle of radius 4 cm, centred at O
(b)a square with sides of 4 cm, centred at O
(c)a straight line 4 cm long, starting at O
(d)two points, each 4 cm from O
14.In a construction, a point P is marked at the foot of the perpendicular drawn from point X to a straight line. Which statement correctly compares the distance XP with the distance from X to any other point on the line?
(a)XP cannot be compared without knowing the line's length
(b)XP equals every other distance from X to the line
(c)XP is the longest distance from X to the line
(d)XP is the shortest distance from X to the line
15.A straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.
(a)a rounded rectangle: 5 m by 4 m with semicircular ends
(b)a circle of radius 2 m
(c)a rectangle, 9 m by 4 m
(d)a rectangle, 5 m by 2 m

Build your own mix at the worksheet builder.