The coordinates of the vertices of RAMP are $R(3,\,0)$, $A(0,\,{-2})$, $M(-5,\,{-2})$, and $P(-5,\,2)$.

(i) Side $AM$ connects $A(0,\,{-2})$ and $M(-5,\,{-2})$, which is a horizontal line. Side $MP$ connects $M(-5,\,{-2})$ and $P(-5,\,2)$, which is a vertical line. Since a horizontal line and a vertical line intersect at a right angle, sides $AM$ and $MP$ are perpendicular to each other.

(ii) Since points $A$ and $M$ share the same $y$-coordinate ($-2$), side $AM$ is parallel to the $x$-axis. Alternatively, since points $M$ and $P$ share the same $x$-coordinate ($-5$), side $MP$ is parallel to the $y$-axis.

(iii) Points $M(-5,\,{-2})$ and $P(-5,\,2)$ have the same $x$-coordinate but opposite $y$-coordinates. This indicates they are equidistant from the $x$-axis and on opposite sides, making points $M$ and $P$ mirror images of each other in the $x$-axis.