Name two invariant points under reflection in the x-axis. 

The point $\mathrm{P} (5,3)$ was reflected in the origin to get the image  $\mathrm{P}\text{'}$.

Write down the co-ordinates of $\mathrm{P}\text{'}$.

The point $\mathrm{P} (5,3)$ was reflected in the origin to get the image $\mathrm{P}\text{'}$.

If $\mathrm{M}$ is the foot of the perpendicular from $\mathrm{P}$ to the $x-$axis, find the co-ordinates of $\mathrm{M}$

The point $\mathrm{P} (5,3)$ was reflected in the origin to get the image  $\mathrm{P}\text{'}$.

If $\mathrm{N}$ is the foot of the perpendicular from $\mathrm{P}\text{'}$ to the x-axis, find the co-ordinates of $\mathrm{N}$

The point $\mathrm{P} (5,3)$ was reflected in the origin to get the image  $\mathrm{P}\text{'}$.

Name the figure $\mathrm{PMP}\text{'}\mathrm{N}$.

The point $\mathrm{P}(3,4)$ is reflected to $\mathrm{P}\text{'}$ in the$x-$axis; and $\mathrm{O}\text{'}$ is the image of $\mathrm{O}$ (the origin) when reflected in the line $\mathrm{PP}\text{'}$. Write the coordinates of $\mathrm{P}\text{'}$ and $\mathrm{O}\text{'}$.

The point $\mathrm{P}(3,4)$ is reflected to $\mathrm{P}\text{'}$ in the x-axis ; and $\mathrm{O}\text{'}$ is the image of $\mathrm{O}( \mathrm{the} \mathrm{origin} )$ when reflected in the line $\mathrm{PP}\text{'}$. Write the length of the segments $\mathrm{PP}\text{'}$ and $\mathrm{OO}\text{'}$.

The point $\mathrm{P}(3,4)$ is reflected to $\mathrm{P}\text{'}$ in the x-axis ; and $\mathrm{O}\text{'}$ is the image of $\mathrm{O}( \mathrm{the} \mathrm{origin} )$ when reflected in the line $\mathrm{PP}\text{'}$. Write:

The geometrical name of the figure $\mathrm{POP}\text{'}\mathrm{O}\text{'}$.

$\mathrm{P}$ and $\mathrm{Q}$ have co-ordinate $\left(0,5\right)$ and $\left(- 2,4\right)$.

$\mathrm{P}$ is invariant when reflected in an axis. Name the axis.