A grid PQRS is distorted such that its edges get stretched or compressed \textbf{UNIFORMLY to form \(P'Q'R'S'\) as shown on the left. Identify the correct distorted grid from the options.}
Show Hint
For uniform distortion problems:
\begin{itemize}
\item Straight lines must stay straight,
\item Parallel lines must remain parallel,
\item Look for smooth, consistent spacing changes across the grid.
\end{itemize}
Step 1: The key condition is that the grid is distorted by \emph{uniform stretching or compression}.
This means:
\begin{itemize}
\item Straight lines must remain straight,
\item Parallel lines must remain parallel,
\item Spacing between grid lines changes smoothly and consistently.
\end{itemize}
\bigskip
Step 2: Observe the mapping from \(PQRS\) to \(P'Q'R'S'\) on the left.
The deformation is continuous and affine-like, with no bending or local warping of grid lines.
\bigskip
Step 3: Check each option for violations of uniform distortion:
\begin{itemize}
\item A: Shows irregular spacing; some grid lines appear locally bent — invalid.
\item B: Non-uniform compression across rows; spacing is inconsistent — invalid.
\item C: Parallelism is not preserved uniformly — invalid.
\item Option D: Preserves straightness, parallelism, and smooth variation of spacing — valid.
\end{itemize}
\bigskip
Final Answer:
\[
\boxed{D}
\]
\bigskip
