Chapter 1.1, Problem 2E

To determine

To find: The two different graphs.

Answer to Problem 2E

Second and fourth figures.

Explanation of Solution

Given information: A graph and four statements.

Calculation:

In the graphs below, red colored figure represents the initial state, blue color represents intermediate state and green colored figure represents the final state,

For first statement,

The transformation of coordinates is like,

  $\begin{array}{l}(1,-2)\to (1,2)\to (3,2)\\ (3,-2)\to (3,2)\to (5,2)\\ (1,-4)\to (1,4)\to (3,4)\\ (3,-4)\to (3,4)\to (5,4)\end{array}$

  

For second statement,

The transformation of coordinates is like,

  $\begin{array}{l}(1,-2)\to (1,4)\to (3,4)\\ (3,-2)\to (3,4)\to (5,4)\\ (1,-4)\to (1,2)\to (3,2)\\ (3,-4)\to (3,2)\to (5,2)\end{array}$

  

For third statement,

The transformation of coordinates is like,

  $\begin{array}{l}(1,-2)\to (3,-2)\to (3,2)\\ (3,-2)\to (5,-2)\to (5,2)\\ (1,-4)\to (3,-4)\to (3,4)\\ (3,-4)\to (5,-4)\to (5,4)\end{array}$

  

For fourth statement,

The transformation of coordinates is like,

  $\begin{array}{l}(1,-2)\to (3,4)\to (1,-4)\\ (3,-2)\to (5,4)\to (3,-4)\\ (1,-4)\to (3,2)\to (1,-2)\\ (3,-4)\to (5,2)\to (3,-2)\end{array}$

  

Clearly, the final stage of fourth statement is visibly different than the others.

While, final stage of first, second and third statements look same but the transformation of the vertices of the second is different than first and third, i.e. vertices occupy different positions.

Thus, answer is second and fourth figures.