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1. Perpendicular bisector
Set the distance between the point of the compasses and the pencil to be more than half the length of the line
Place the point of the compasses on one end of the line and sketch an arc above and below the line
Keeping your compasses set to the same distance, move the point of the compasses to the other end of the line and sketch an arc above and below it again, the arcs should intersect each other both above and below the line
Connect the points where the arcs intersect with a straight line
2. Perpendicular to a line, from a point
Set the distance between the point of your compasses and the pencil to be greater than the distance between the point P and the line
Placing the point of the compasses onto the point P, draw an arc that intersects the line in two places
Make sure that the distance between the point on the compasses and the pencil is greater than half the distance between the two points of intersection, place the point of the compasses on to one point of intersection and sketch an arc above and below the line
Keeping the distance between the point on the compasses and the pencil the same, move th point of the compasses onto the other point of intersection and again draw an arc both above and below the line, these should intersect with the previous arcs
3. Angle bisector
It shows a region on a map/diagram that is closer to one side than another
Open the compasses, the distance between the point and the pencil is not particularly important but setting them about half the distance of the lines forming the angle is reasonable
Placing the point of the compasses at the point of the angle, sketch an arc that intersects both of the lines that form the angle
Set your compasses to the distance between these two points of intersection, place the point of the compasses on one of the points of intersection and sketch an arc
Keeping the distance between the point of the compasses and the pencil the same, place the point of the compasses on the other point of intersection and sketch an arc, this should intersect the arc sketched in STEP 3
On triangle ABC below, indicate the region that is closer to the side AC than the side BC.
This question is asking for the region that is closer to one side of an angle than the other, so an angle bisector is needed.
Open your set of compasses to a distance that is approximately half the length of the sides AB and AC.
This distance is not too important, but keeping it the same length throughout the question is very important.
Place the point of the compasses at A and draw arcs across the lines AB and AC. Be very careful not to change the length of the compasses as you draw the arcs.
Leaving the compasses open at the same length, put the point at each of the places where the arcs cross the sides AB and AC and draw new arcs which cross over each other in the middle.
Draw a line from A to the point where the arcs cross over each other (this will not usually be directly on the third side of the triangle and never has to be!)
Shade the region between the angle bisector (the line you have drawn) and the side AC.
A house lies between Town A and Town B as shown on the scale diagram below.
Two masts, located at the points R and S, provide the area shown on the map with radio signals.
The house will receive its radio signal for the mast located at point R if it is either…
… closer to Town A than Town B, or…
… outside a region 5 miles from the mast at point S.
Showing your working carefully on the scale diagram below, determine whether the house receives radio signals from the mast at point R or the mast at point S.
Begin by finding the region satisfying the first condition, that the house is closer to Town A than Town B.
This is found by constructing the perpendicular bisector of the line segment that joins Town A and Town B. You will need to add this line segment in yourself before starting.
Open your compasses to more than half of the distance from Town A to Town B and draw arcs both above and below the line joining Town A to Town B.
Do this from both the point at Town A and the point at Town B. The arcs should cross over each other.
The perpendicular bisector is the line that passes through both of the points where the arcs cross over each other.
The house is on the same side of the perpendicular bisector as Town B is.
The house is closer to Town B than Town A.
Now check the second condition, to see if the house is further than 5 miles from the mast at point S.
To find the locus of points exactly 5 miles from point S, first consider the scale given on the scale drawing.
1 cm = 1 mile
5 cm = 5 miles
Open your set of compasses to exactly 5 cm. Measure this carefully using a ruler.
Being extra careful not to change the length of your compasses, put the point at S and draw a circle around S with a radius of 5 cm. You may not be able to draw the full circle, but make sure you have the part that is near the point where the house is located.
The house is located outside of this region, so it is more than 5 miles from the mast at the point S.
The house only satisfies one of the conditions given to receive its signal from the mast at point S.
The house receives its radio signal from the mast at point R.