Question

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.}

• A. A
• B. B
• C. C
• D. D

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}

Answer 1

The Correct Option is D

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