M17 | Maths Made Easy

M17

Question: Bill is planning to put a fountain in his garden. His house is situated along the line CD, and there is a tree at point E. He wants the fountain to be at least 3m away from his house and at least 1.5m away from the tree. Shade the locus of points where he could have the fountain.

 

Answer: For the fountain to be at least 3m away from his house along CD, we need to only consider the area to the left of the straight line which is parallel to CD and 3cm away from it.

Then, the locus of points which are 1.5m away from the tree at E will be a circle of radius 1.5cm – for the fountain to be at least 1.5m away, it must be outside this circle.

So, the locus of points where he could place the fountain is to the left of the (blue) line 3m away from the house, and outside the (green) circle which is 1.5m away from the tree. The correct region is shaded red on the picture below.