Cellular phone towers in a town are represented by the oxeembq1z)6+points P, Q, R, and S (not shown) in the partially complete Voronoi diagram shown below. The regions created by the diagram representm zbqex)6 e+1o the phone coverage provided by each tower.



1.Write down the coordinates of the missing phone tower S. (a,b) a=   b=  
2.Calculate the coverage area provided by phone tower Q. A =    $km^2$
3.Find the gradient of the edge of Voronoi diagram between towers Q and R. $m_{e,QR}$ =   
The phone towers provide different data download speeds, as per the table below.


Tower is P ;Data download speed is 25 MBps ;Tower is R ;Data download speed is 30 MBps ;Tower is Q & S ;Data download speed is 20 MBps ;
4.A customer is located at (4,10). Determine the download speed she receives.

  Consider the Voronoi dim uppa3k+im cq:*b0x-7 /jehx agram below with sites A, B, C and D, and intersections E and xm0up7i*em:bc -x kj3+pa h q/F.



1.Determine the site closest to the coordinate (9,6).
2.Determine the coordinates of the centre of the largest empty circle.
3.Calculate the area of the largest empty circle. a ≈    $units^2$

  Points A(1,5)，B(5,9),C(7,7),D(9,3) and E(13,11) represent feeding-racks forj gzz5zvdk1+a/ j -s*mgj52os dears in the Teutoburg Forest in Germany. The feeding-5 vg 1j-/g zasosmjzk *d2+z5jracks are illustrated in the following coordinate axes.
Horizontal scale: 1 unit represents 1 km.
Vertical scale: 1 unit represents 1 km.

1.Calculate the gradient of the line segment CE.
Three straight lines are drawn on the coordinate axes to form an incomplete Voronoi diagram. $m_{CE}$ = $\frac{a}{b}$ a =    b =   
2.Find the equation of the line that would complete the Voronoi cell containing site C. Give your answer in the form
ax+by+d=0 where a,b,d∈Z. ax+by+c=0 a =    b =    c =   

3.In the context of the question, explain the meaning of the Voronoi cell containing site C.

  Points A(−3,5), B(5,3), C(3,9), D(3,−3) and E(11,5) repret-2,ukosza * ysent coffee shops in a city. The coffee shops are illustrated on the follo*2ysoutk- , azwing coordinate axes.
Horizontal scale: 1 unit represents 1 km.
Vertical scale: 1 unit represents 1 km.



1.Calculate the gradient of the line segment BE.
The diagram below shows three straight lines that form an incomplete Voronoi diagram.



2.Find the equation of the line completing the Voronoi cell containing site B. Give your answer in the form ax+by+d=0 where a,b,d∈Z. ax+by+c=0 a =    b =    c =   
3.In the context of the question, explain the meaning of the Voronoi cell containing site B.

  The Voronoi diagram below shows four hotels in a small town represented by point,o iv.yix1on7b -zx5uvp-r; i hq. k;ss with coordinates A(−4,4), B(3,5), C(3,−3), ands;hzx ,rpi qb niv-y1. 5oo;-x7ku.vi D(−1,3). The vertices $V_1$​, $V_2$​ and $V_3$​ are also shown. Distances in the direction of the x and y axes are measured in increments of 100 metres.

  Consider the Voronoi diagram below for a citx,vvls 6 1qh+cnq0c t;y that contains the towns A, B, C, an0htq+ccx6nq;vv 1, lsd D.
The equation of the perpendicular bisector between sites A and D, PB(A,D), is found to be
y=x−25​

1.Determine the equation of the perpendicular bisector between C and D, PB(C,D).y =-$\frac{a}{b}$x+$\frac{c}{d}$ a =    b =    c =    d =   
2.Hence, determine the coordinates of the intersection $V_2$​. (a,b) a=   b=  
3.Determine the optimal position for a toxic waste dump in this city, such that it is as far away from a town as possible.

  Consider the Voronoi diagra5e b55o kio)k yrm uv9udlb+3*m below that shows the location of convenient stores within a town. The convenient stores are labelled A, B, C, and D. i +lbdm5*3k9okv br5yeou5)u
The equation of the perpendicular bisector between sites A and D, PB(A,D), is found to be
y=−x+6​






1.Determine the equation of the perpendicular bisector between sites C and D, PB(C,D).y =$\frac{a}{b}$x-$\frac{c}{d}$ a =    b =    c =    d =   
2.Hence, determine the coordinates of the intersection $V_1$​.
A company that opens and manages convenient stores wants to open a new store in this town. (\frac{a}{b},\frac{c}{d}) a =    b =    c =    d =   
3.Determine the optimal position for this new store, so that it is as far as possible from its nearest store.

  A town currently has four Ita4pn g/u 2;6o7q8 4f+czr 7mnm vdfixmclian pizza restaurants. A famous chef wishes to open a new pizza restaurant in the town but wants it to be located as far away as possible from the four cuq 7d7xr ; mmf/vo+cui4cn24gpmznf86 rrent restaurants.
The Voronoi diagram below showing the positions of the four current restaurants on a set of coordinates axes: A(2,3) B(8,4), C(7,1), and D(2,1), where one unit represents 1 km.



1.Write down the coordinates of P. (a,b) a=   b=  
2.Show that the coordinates of Q are(5.03,3.32), correct to three significant figures.(a,b) a=   b=  
3.Determine where the famous chef should position their new restaurant.

4.Determine the estimated average weekly number of pizzas this new shop will sell. ≈    pizzas

  The Voronoi diagram belo703wgh)vg s i ird0uv2w shows the location of fire stations in outback Queensland, a Northvhigrvw0) dg0s23i u7-Eastern state of Australia.
Horizontal scale: 1 unit represents 100 km.
Vertical scale: 1 unit represents 100 km.



1.Identify the nearest fire-station to houses located at
(1)(300,300)   
(2)(−200,100)   
A house located at (200,200) has an internal fire and requires assistance.
2.Determine which fire-stations the house is closest to.    and   
3.Determine how far the house is from these two fire-stations. Give your answer to the nearest kilometre. d ≈    km

  The Voronoi diagram below shows ty(: fjo; ax8(1i mruj7o wi7kxhe location of fire stations in outback Queensland, a North-Eas7: rjx mu1oi;jow(iyxk7 8a (ftern state of Australia.
Horizontal scale: 1 unit represents 100 km.
Vertical scale: 1 unit represents 100 km.



1.Identify the nearest fire-station to houses located at
(1)(300,300)   
(2)(−200,100)   
A house located at (200,200) has an internal fire and requires assistance.
2.Determine which fire-stations the house is closest to.    and   
3.Determine how far the house is from these two fire-stations. Give your answer to the nearest kilometre. d ≈    km

  The Voronoi diagram below shows the fitness s7gq9nv d(xqy) tudios A, B and C, located in a particu )xn9 g(7dqvyqlar district.



1.On the diagram, shade the cell with the missing fitness studio.
2.Determine the coordinates of the missing fitness studio, D.
3.Jennifer lives an equal distance from fitness studios A and D. Find the shortest possible distance Jennifer's house could be from fitness studios A and D. d ≈    km

  The sites A, B (not shown), C, and D in the Voronoi diagram below represe3 ry):cu:1tt( 9ex8h svoqse knt the location of rainfall recording gauges on a large cornts1et(xh:) u9o:3k8vercqs y farm in Texas, USA.
Horizontal scale: 1 unit represents 1 km.
Vertical scale: 1 unit represents 1 km.

1.Site B is missing from the diagram. Write down its coordinates. B : (a,b) a=   b=  
2.Calculate the area of the cell C. A =    $km^2$
3.Find the distance from point E(9,8) to the nearest rainfall recording gauge.
The table below shows measurements of the average monthly rainfall (mm) of each of the recording gauges. d =    km

4，Estimate the average monthly rainfall at point F(1,6) in mm.    mm