Question:
Lines of the same length and dots of the same size are used to form figures that follow a pattern. The first four figures are shown below.
The table below shows the number of lines and dots used for each figure.
(a) Complete the table for figure 5.
(b) Seventy-two lines are used for one of the figures. What is its figure number?
Solution:
![P6 / ACS / 2019 / CA1 – Q16 [2 marks]](https://i0.wp.com/sgprimaths.com/wp-content/uploads/2021/01/P6_ACS_2019_CA1_Q16-Qns.jpg?resize=400%2C260&ssl=1)
i do not understand the method you use to solve ( b )
Hi! Apologies if the solution is not that clear.
Let me try to explain it further here.
The pattern is observed as such.
For every increase of 2 Figure Number (e.g. from Figure 1 to Figure 3), the Number of Lines increase by 12 (7 + 5).
The initial number of lines = 12.
The final number of lines = 72.
Therefore, we need to find out, how many increase of Figure number would allow the initial number of 12 to increase to 72.
The increase (which is the difference) = 72 – 12 = 60.
Increase of 12 lines -> Increase of 2 Figure Number
Increase of 60 lines -> Increase of 2 x 5 = 10 Figure Number
Initial Figure number = 1
Final Figure number = 1 + 10 = 11.
Hope this clarifies!