The diagram shows triangle RST.

(a) Measure and write the size of angle BSL.
(b) Q is the point where the angle bisectors of R, S, and T meet.
Mark and label the position of the point Q.
(c) (i) M is the mid-point of TR and N is the mid-point of RS.
Measure the distance, x cm, of line MN from Q.
(ii) Shade the region that is:
Less than x cm from Q,
Nearer to TR than to TS, and
Nearer to RT than to RS.

Construct the bisector of angle PQR in the triangle.

The diagram shows the position of the two houses X and Y and a path P.

1 cm represents 25 m.
A public phone is installed such that it is:
• less than 125 m from X
• nearer to Y than X
• more than 100 m from the path
Using ruler and compasses only, find the region where the public phone can be placed. Label it T.

The diagram shows a triangle ABC.

(a) Measure and write:
(i) The length of BC,

(ii) The bearing of A from B.

(b) (i) By construction, show all the points, inside triangle ABC, that are:
(a) 1.5 cm from AC,
(b) Equidistant from C and A.
(ii) Shade the region, inside triangle ABC, of points that are:
More than 1.5 cm from AC
and
Nearer to C than to A.

The diagram shows the points B, C and D and straight lines DC and CB.

(a) A point A is such that AB = 10 cm and AD = 7.2 cm.
By construction, complete the quadrilateral ABCD.
(b) The point O, inside ABCD is:
Equidistant from points B and C,
Equidistant from points C and D.
Locate the point O.
(c) Draw the circle radius OA, centre O.

The diagram represents a triangular field ABC. Scale 1 cm to 50 m.

(a) Find the actual distance from A to B.

(b) Construct the locus of all points, inside the field, that are:
(i) 150 m from AB,
(ii) Equidistant from AB and BC.
(c) A tree is to be planted inside the field so that it is:
less than 150 m from AB, and closer to BC than AB.
Shade the possible region in which the tree can be planted.

The diagram shows a map of four villages A, B, C and D.


(a) Using a scale of 1 cm to represent 2.5 km, make an accurate drawing of the map on the space provided.
CD has been drawn for you.

(b) Measure and write down the size of the angle ABC.

(c) Find the actual distance from village B to C.

(d) Describe the locus of all points that are equidistant from C and D.

(e) Another village E is located on the map such that it is:
7.5 km away from village B,
equidistant from BC and CD,
closer to A than C.
On your scale drawing, by construction, mark the location of the village E.

The diagram shows part of quadrilateral ABCD.

(a) Measure and write the size of reflex angle ABC.

(b) By construction, complete the quadrilateral ABCD such that AD = 6 cm and CD = 9 cm.
(c) A region S inside ABCD, is:
closer to AB than BC and closer to B than A.
Construct and shade the possible region S.

A straight line passes through the points A(0, 2), B(p, 5) and C(8, q).
(a) Given that B is the mid-point of AC, find the value of p.

(b) Find the equation of the line AB.

(c) The length of the line joining A and C is 10 units.
(i) Find the two possible values of q.

(ii) Explain why you would reject one of the solutions of q.