Cellular phone towers in a town are represented dy (qwco2 whef-2,u0x by the points P, Q, R, and S (not shown) in the partiaeof22-0xuc,ww yhdq (lly complete Voronoi diagram shown below. The regions created by the diagram represent 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 diagrj; 24ws hhmfwn++ty c3am below with sites A, B, C and D, and intersections E and F.jhy 3s+;c+h2wt nwfm4



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) rs uc vk7.efv-+tyi*/xepresent feeding-racks for dears in the Teutoburg Forest in Germany. The feeding-racks are illustrated in the followi/yfx7*+kcu- eisvv. tng 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(1cprk -sz+ qi;/1,5) represent coffee shops in a city. The coffee shops are pk+ic;r -zqs /illustrated on 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 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 tow fm4zzc9gtjtci cb-j6 h-+;m/n represented by points with coordinates A(−4,-4 tcm/z-c6 m +fthc9zijg ;jb4), B(3,5), C(3,−3), and 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 city that contains the towns A, B, C, u *bd 7a o9tqql;ag8s1anlqsadq9a;7 g1*8btu o d 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 diagram below that shows the location of convee)jlf,j l* bo su6x)k,nient stores within a town. The convenient stores are labelled A, B, C,)lj,flj),su exk6*o b 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 restauras08*zpw syga5k6or c: nts. A famous chef wishes to open a y gowz ks:a65sr 0c*8pnew pizza restaurant in the town but 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 xarirr ; o3uyf0elg3 u88 n6r*shows the location of fire stations in outback Queensland, a North-Eaxa i3uu*6fo8;0 grlr3ne 8rrystern 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 thsojy 3u m2*w.he location of fire stations in outback Queensland, a North-Eastern state3mu *2 hsjowy. 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 studios A, B anpfj-.suy sz0qh-qo(ze(8 li9s 4 qp1nd C, located in a particular0.on yeh( 4q1fssuisp z9q q-l8 (-jpz 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 represent t5 x dauzyvd5sp d/91m.he location of rainfall recording gauges on a large corn farm in zm vx9au5dy 5d /.p1dsTexas, 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