Draw a pair of axis that will take a whole page. -10 < x < 14, -8 1 To preserve the wellbeing of the animals, the local safari park has decided that cars won't
be
allowed to come too close to the watering hole. For this, they set to draw compulsory tracks
that visitors will have to stay on
The natural park can be considered as a rectangle. A coordinate grid is placed on a map of the
park with the origin at the intersection of its diagonals. The watering holes are situated at
A (6,8), B ( -4,6), C(4,2), D (-6,2), E (-2,6), F ( 12,0), G( 11,6),
Draw the Vornoi to represent the situation. For this you should:
a Find:
i the midpoint of [AB]
ii the gradient of [AB]
iii hence the equation of the perpendicular bisector of [AB]
b Find:
i the midpoint of [AC]
il the gradient of (AC)
ili the equation of the perpendicular bisector of (AC)
c Show that the location of the first crossroad e. g the point of intersection of the two
bisectors, is ) (156)
d Using similar method, find the equation of the perpendicular bisector of:
i (BC) i [BD]
ili [CD]
e hence K the second crossroad e. g the point of intersection of the three bisectors
f Show that the perpendicular bisectors of (BC) and (BD) are perpendicular
Using similar method, find the equation of the perpendicular bisector of:
i (DE) II (CE)
il (CF)
iv (EF)
v (CG) vi (GA]
vii (FG]
h hence L, M, N and P the rest of the crossroads
i A ranger house is to be built in the park as far away as possible from any watering hole.
Determine where it should be built.
2 Toxic waste are stored in shielded containers and buried in the underground vaults such that all
of the different types are as far away as possible from each other.
A coordinate grid is placed on a map of the landfill site with the origin in the south west
corner. If 4 wells A (6,8), B(-4,6), C(4,2), D (-6,2) have already been filled, and a fifth one
need to be dug.
Determine its position using a Vornoi diagram.