If the pressure $P$ and volume $V$ of a gas are related by the equation $P{V}^{\gamma }=\text{constant},$ where $\mathrm{\gamma }$ is a positive constant. Then the graph of $\frac{\left(\frac{dP}{dV}\right)}{P}$versus $V$ will be:

Using a dilation of scale factor $4$, with centre at the origin, find the coordinates of the image $A’$ of the point $A(3,-7)$?

Using a dilation of scale factor $\frac{4}{5}$, with centre at the origin, find the coordinates of the image $C’$ of the point $C(20,0)$?

Find the scale factor of dilation (with centre at the origin) if point $F\left(0,-70\right)$ becomes $F\text{'}\left(0,21\right)$? And, Write using correct notation.

Using a dilation of scale factor $5$, with centre at the origin, find the coordinates of the image $L’$ of the point $L(12,-9)$?

Find the scale factor of dilation (with centre at the origin) if point $E\left(48,-20\right)$ becomes $E\text{'}\left(12,-5\right)$? And, write its notation.

Using a dilation of scale factor $\frac{1}{3}$, with centre at the origin, find the coordinates of the image $B’$ of the point $B(-12,27)$?

What is the scale factor of dilation (with center at the origin) if the image of point $T(6,-18)$ is $T’(2,-6)$? (write answer in fraction)

Find the scale factor of dilation (with centre at the origin) if point $D(9,13)$ becomes $D’(27,39)$? 

This is an example of a fractal design. In math, a fractal is an abstract object formed by a never-ending pattern repeated at increasingly small scales.

Describe the dilations that you see in the fractal design.

The graph of $y=f\left(x\right)$ is symmetrical about the line $x=1$, then

Describe the transformation that has occurred to create the image in the diagram below.

Find the scale factor of dilation (with centre at the origin) if point $F\left(0,-70\right)$ becomes $F\text{'}\left(0,21\right)$? (write answer in fraction)

What do you think a negative scale factor indicates? Explain.

Describe the transformation that has been performed in the diagram and express it using correct arrow notation.  

Find the scale factor of dilation (with centre at the origin) if point $D(9,13)$ becomes $D’(27,39)$? And, write its correct notation.