Loci and constructions

1

What does it mean to bisect an angle or a line?

2

Which diagram shows an accurate locus of points closer to A than B?

3

Which diagram shows the triangle ABC where side AC is 4 cm, angle A is 40° and angle C is 70°?

4

Which diagram shows the triangle PQR where side PQ is 7 cm, side QR is 9 cm and angle Q is 50°?

5

Questions 5 - 10 are for Intermediate and Higher tier

What scenario does this construction best fit?

A rectangle with points W, X, Y and Z divided up by two curved lines

6

Which criteria best defines the shaded area?

A triangle with points A, B and C divided up by three lines

7

Which constructions are used to create this locus?

A triangle with points A, B and C divided up by four lines

8

What construction should you use to show the locus of points equidistant from AB and AC in the trapezium ABCD?

A trapezium with points marked as A, B, C and D

9

What construction should you use to show the locus of points equidistant from AB and CD in the rectangle ABCD?

A rectangle marked with points A, B, C and D

10

There are four possible locations of buried treasure shown on this map:

A trapezium with points marked as A, B, C and D with dotted lines marked 1, 2, 3 and 4

Here are two clues:

  • The treasure is buried equidistant from the line DA to the line DC
  • The treasure is closer to the point D than B

Where is it buried?