Chapter 1.8, Problem 30E

a.

To determine

To identify : the coordinates of each of the stones shown in the diagram.

Answer to Problem 30E

The coordinate of the black stone is $\left(3,\text{ 2}\right)$ and the coordinate of the white stones are $\left(3,\text{ 1}\right)$ , $\left(3,\text{ 3}\right)$ , $\left(2,\text{ 2}\right)$ and $\left(4,\text{ 2}\right)$ .

Explanation of Solution

Solution :

From the provided diagram it can be observed that the location of the black stone is 3 units right to the origin and then 2 units up.

Therefore, the coordinate of the black stone is $\left(3,\text{ 2}\right)$ .

Similarly, the coordinate of the white stones are $\left(3,\text{ 1}\right)$ , $\left(3,\text{ 3}\right)$ , $\left(2,\text{ 2}\right)$ and $\left(4,\text{ 2}\right)$ .

Hence,

The coordinate of the black stone is $\left(3,\text{ 2}\right)$ and the coordinate of the white stones are $\left(3,\text{ 1}\right)$ , $\left(3,\text{ 3}\right)$ , $\left(2,\text{ 2}\right)$ and $\left(4,\text{ 2}\right)$ .

b.

To determine

To find : A stone is placed at $\left(-3,\text{ 2}\right)$ . Give the coordinate of the points that the player must cover with black stones to capture the white stone.

Answer to Problem 30E

The coordinate of the black stones must be $\left(-3,\text{ 1}\right)$ , $\left(-3,\text{ 3}\right)$ , $\left(-4,\text{ 2}\right)$ and $\left(-2,\text{ 2}\right)$ .

Explanation of Solution

Given information :

Consider, the position of the white stone provided in the question,

  $\left(-3,\text{ 2}\right)$

Calculation :

Since the position of the white stone is $\left(-3,\text{ 2}\right)$ .

Therefore, to capture the white stone the coordinates of the black stones must be $\left(-3,\text{ 1}\right)$ , $\left(-3,\text{ 3}\right)$ , $\left(-4,\text{ 2}\right)$ and $\left(-2,\text{ 2}\right)$ .

Hence,

The coordinate of the black stones must be $\left(-3,\text{ 1}\right)$ , $\left(-3,\text{ 3}\right)$ , $\left(-4,\text{ 2}\right)$ and $\left(-2,\text{ 2}\right)$ .