1. **Problem Statement:** We have a figure P with points A(2,4), B(4,4), C(6,4), and D(1,2). The figure undergoes a transformation to image Q with points A'(4,2), B'(4,4), C'(4,16), and D'(2,7). 2. **Describe the transformation:** The transformation maps each point $(x,y)$ of P to $(y,x)$ in Q. 3. **Formula for reflection about the line $y=x$:** $$ (x,y) \to (y,x) $$ This means the x- and y-coordinates are swapped. 4. **Check points:** - $A(2,4) \to A'(4,2)$ correct. - $B(4,4) \to B'(4,4)$ correct (point on the line $y=x$ remains the same). - $C(6,4) \to C'(4,6)$ but given $C'(4,16)$ seems inconsistent; assuming typo, correct reflection is $(4,6)$. - $D(1,2) \to D'(2,1)$ but given $D'(2,7)$ inconsistent; assuming typo, correct reflection is $(2,1)$. 5. **Conclusion:** The transformation is a reflection about the line $y=x$. 6. **Graphing instructions:** - Draw the line $y=x$. - Plot points A, B, C, D. - Reflect each point about $y=x$ to get A', B', C', D'. - Connect points to form triangles P and Q. Final answer: The transformation is a reflection about the line $y=x$ which swaps the coordinates of each point.