Chapter 2.4, Problem 14E

(a)

To determine

$y=\left(1.0091\right){\left(0.9805\right)}^x$

To draw:

The graph of the given vertices.

Explanation of Solution

Given:

The vertices is

  $A\left(-1,0\right),B\left(0,1\right),C\left(1,0\right),D\left(0,-1\right)$

Concept used:

To draw the graph of the given a square with vertices

Calculation:

The graph

Graph of the original and dilated squares.

In order to get $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$ multiply each coordinate of the original square by the dilation factor

The dilation of $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$ by $3$ to $A^{″}{B}^{″}{C}^{″}{D}^{″}$ multiply each coordinate of $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$ by $3$ .

The net dilation is a dilation of $ABCD$ by a factor of $6$ to get $A^{″}{B}^{″}{C}^{″}{D}^{″}$

(b)

To determine

To draw:

The graph of the second coordinate plane.

Explanation of Solution

Given:

The vertices is

  $A\left(-1,0\right),B\left(0,1\right),C\left(1,0\right),D\left(0,-1\right)$

Concept used:

To draw the graph of the given a square with vertices

Calculation:

Draw the graph on the second coordinate plane

The dilation of square $ABCD$ after a dilation of scale factor $3$ .

(c)

To determine

To compare:

The results of the given part (a) and part (b).

Explanation of Solution

Given:

The vertices is

  $A\left(-1,0\right),B\left(0,1\right),C\left(1,0\right),D\left(0,-1\right)$

Concept used:

To draw the graph of the given a square with vertices

Calculation:

The end result for dilation are equal.

This observation is hypothesized the statement below.

Dilation is associative.

This means that is $A$ is matrix.

So,

  $a\left(b\left(A\right)\right)=ab\left(A\right)$

Where $a$ and $b$ are scale.