CPM Homework Help : ACC6 Problem 8-105

Copy the dot pattern below and draw Figures $0$ , $4$ , and $5$ . Explain how you could know the number of dots in any figure if you knew the figure number.

$\begin{array}{c c c} \newcommand{blank}{\ } & \bullet\\ \bullet & \bullet & \bullet\\ \newcommand{blank}{\ } & \bullet\\ \end{array}\\ \text{Figure 1}$

$\begin{array}{c c c c c} \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \bullet & \bullet & \bullet & \bullet & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet \end{array}\\ \quad \;\,\text{Figure 2}$

$\array{ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet\\ \newcommand{blank}{\ } & \newcommand{blank}{\ } & \newcommand{blank}{\ } & \bullet}\\ \qquad \quad \text{Figure 3}$

Hint 1:

Could you write an expression to find the number of dots in a figure?

Hint 2:

Look at Figure 2 to the right where $4$ groups of $2$ dots (the figure number) are circled and and the middle dot is left over. Figure 2 has 4 arms, each with 2 dots circled, plus a dot in the middle dot.
An expression representing the number of dots in this figure would be $1 + 4x$ , where $x$ is the figure number.
Use this to help you draw the next figures.