The diagram is a scale drawing of a field. The actual length of the side AB is 100 metres.

Question

( a ) Write the scale of the drawing in the form 1 : n, where n is an integer.

[1]

( b ) In this part use a straight edge and compasses only.
Leave in your construction lines.

( i ) A tree in the field is equidistant from the point A and the point D.
Construct the line on which the tree stands. [ 2 ]

( ii ) The tree is also equidistant from the sides BC and CD.
After constructing another line, mark the position of the tree
and label it T. [ 3 ]

Answer 1

(a) The scale of the drawing is 1 : 10.

(b)
(i)
- Use a compass to measure the distance from point A to point D.
- Place the compass on point A and draw an arc that intersects the line segment AB.
- Place the compass on point D and draw an arc that intersects the line segment AB.
- Draw a straight line that connects the two intersection points. This line is the line on which the tree stands.

(ii)
- Use a compass to measure the distance from point B to point C.
- Place the compass on point B and draw an arc that intersects the side CD.
- Place the compass on point C and draw an arc that intersects the side BC.
- Draw a straight line that connects the two intersection points. This line is the other line on which the tree stands.
- Mark the position of the tree on the intersection of the two lines and label it T.