Cellular phone towers in a town are represented by the p s+ um wkd959:;qnh vpsndx;jj08 q0kwoints P, Q, R, and S (not shown) in the partially complete Voronoi diagram shown below. The regions created by the diagram represent the phone coverage provided by eacd9md ;+nvwhn 90 xq pujswqkjs0:k; 58h 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 diagram below with sites A, B, C zum1zr3t3 +gc and D, and intersections E and Fg3cmzz3 1tr u+.



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 fo ,gb1;zbpxn .ar dears in the Teutoburg Forest in Germany. The feeding-racks are illustratebbag 1pn.,zx ;d 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) repr0.8fgsp . wmcdh3lvqlu-3r -gesent coffee shops in a city. The coffee shops are illustrated on the following coordinateh-cllsf-m3.v8upr w gg.3q0d 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 sh4fk .zvd(8m: ac/jaf fows four hotels in a small town represented by points with coordinates A(−4,4), B(3,5), C(3,−3), and D(−1,3). Tm4za/ d j(f8k.af:f vche 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 city that contains the towns A, 9 m7mz- qw8m8 07u 5rbgyh:xdoq;vb eiB, C, and D. bo0q7whm: qrbm9 5-7yd8i ez gmuvx8;
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 diagram below the d/l6o f:n9wwat shows the location of convenient stores within a / 6wdoe9wlnf: town. The convenient stores are labelled A, B, C, and D.
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 Italian pizza restaurants. A famoa8 25bh6stwl cqxh f52miq f52us chef wishes to open a new pizza restaurant in the town q qxm5lc ifs5tw62f2ab 52h8hbut wants it to be located as far away as possible from the four current 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 below shows the location of fire stations in outbackrctkhx3:i7r:w,42 kh33wob f: hfvkv Queensland, a North-E:rok:v h 4h 32fkwxv f wb73rkih,3:tcastern 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 locf0plij54 . pakation of fire stations in outback Queenslanl45ppji kaf.0 d, a North-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 belowj-y8cbzs5q;zmkq . r:6k-xw w shows the fitness studios A, B and C, located in a particular district. zkyk-q ;b8xq j-:.r 6mcsww5z



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 dij 2zh8ru0fdmoyu. 96 tagram below represent the location of rai2m thjuf.68 zouy 9dr0nfall recording gauges on a large corn 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