Question 13:
Five friends were asked which activities they like from bowling, badminton and hiking. Table 9.1 shows which of these activities each of the five friends like. Diagram 7.1 shows an incomplete graph to represent the information in Table 9.1.
(a) State the label which should be used for:
(i) Vertex Q,
(ii) Edge k.
[2 marks]
(b) Fahad and his friends plan to tour Malacca city. Table 9.2 shows information about the places in the city and Table 9.3 shows the distances between them.
(i) Complete the Diagram 7.2 in the answer space by drawing an undirected and weighted graph to represent their journey. [3 marks]
(ii) Hence, draw a tree with a minimum total weight such that every place being visited once only. [2 marks]
(iii) Fahad wants to go to Klebang Beach from the Zoo. He must pass through the Hang Tuah’s Well to fetch his brother. List the two shortest routes for this journey. [2 marks]
Solution:
(a)(i)
Both Suzi and Suria like bowling, therefore activity P is bowling. Other than bowling, Suria like hiking as well, thus, vertex Q is hiking.
(a)(ii)
As the third activity R is badminton, the person that likes both badminton and hiking is Pandian, thus, k is Pandian.
(b)(i)
(b)(ii)
Minimum total weight of every place being visited once only:
(b)(iii)
\begin{aligned} \text { First shortest route } & =10.1+7.5+6.2+9.2=33 \mathrm{~km} \\ & =Z \rightarrow B \rightarrow P \rightarrow A \rightarrow K \\ \text { Second shortest route } & =11.2+7.2+6.2+9.2=33.8 \mathrm{~km} \\ & =Z \rightarrow R \rightarrow P \rightarrow A \rightarrow K\end{aligned}
Five friends were asked which activities they like from bowling, badminton and hiking. Table 9.1 shows which of these activities each of the five friends like. Diagram 7.1 shows an incomplete graph to represent the information in Table 9.1.
(a) State the label which should be used for:
(i) Vertex Q,
(ii) Edge k.
[2 marks]
(b) Fahad and his friends plan to tour Malacca city. Table 9.2 shows information about the places in the city and Table 9.3 shows the distances between them.
(i) Complete the Diagram 7.2 in the answer space by drawing an undirected and weighted graph to represent their journey. [3 marks]
(ii) Hence, draw a tree with a minimum total weight such that every place being visited once only. [2 marks]
(iii) Fahad wants to go to Klebang Beach from the Zoo. He must pass through the Hang Tuah’s Well to fetch his brother. List the two shortest routes for this journey. [2 marks]
Solution:
(a)(i)
Both Suzi and Suria like bowling, therefore activity P is bowling. Other than bowling, Suria like hiking as well, thus, vertex Q is hiking.
(a)(ii)
As the third activity R is badminton, the person that likes both badminton and hiking is Pandian, thus, k is Pandian.
(b)(i)
(b)(ii)
Minimum total weight of every place being visited once only:
(b)(iii)
\begin{aligned} \text { First shortest route } & =10.1+7.5+6.2+9.2=33 \mathrm{~km} \\ & =Z \rightarrow B \rightarrow P \rightarrow A \rightarrow K \\ \text { Second shortest route } & =11.2+7.2+6.2+9.2=33.8 \mathrm{~km} \\ & =Z \rightarrow R \rightarrow P \rightarrow A \rightarrow K\end{aligned}