1. John wants to stand exactly the same distance away from the Ash tree and the Oak tree. Where should John stand?

2. How can we represent the path that the ship should take accurately?
The ship wants to keep as far away from the rocks as possible at all times. What path should the ship take?
How can we represent the path that the ship should take accurately?
Students may suggest that we measure the distance between the points and mark half way and draw a line through this. Encourage them to try this and see if they choose any point on the line is it exactly the same distance?

3. The ship wants to keep as far away from the rocks as possible at all times. What path should the ship take?
We need to make sure the path that we draw is equidistant from the two rocks

4. To do this we can use a construction.
The ship wants to keep as far away from the rocks as possible at all times. What path should the ship take?
To do this we can use a construction.
This is known as a perpendicular bisector.
Can you think why?

5. The Perpendicular Bisector
Perpendicular: At right angles (900) Bisector: Split into equal parts

6. Constructing a perpendicular bisector
Every point on this new path is exactly the same distance from the point P as it is from the point Q
Try it!
Complete the perpendicular bisector and take a measurement from a point on your path to P and Q
Is it the same? P Q

7. The Perpendicular Bisector
Construct the perpendicular bisector of each of the lines on the worksheet. Complete your constructions on the worksheet Leave in your construction lines

8. Extension
Draw a triangle and construct the perpendicular bisector of each side
You should find that the bisectors intersect at a single point, either inside or outside the circle!
Now using the point of intersection as centre, draw the smallest possible circle that does not enter the triangle
You should find that the circle touches all three corners of the triangle
This works with any triangle…

9. Using a compass and ruler only can you construct a 90 and 45 degree angle with a perpendicular bisector
Right-angle
45o angle
Draw a perpendicular bisector
Bisect a 90o angle from a perpendicular bisector