1. **Problem Statement:** We have a rectangle AUNT with dimensions $AU=6$ cm (width) and $UN=3$ cm (height). Point $J$ lies on the line extended from the bottom edge $NT$ but outside the rectangle such that $TJ = UI$. Point $M$ is the symmetric of $N$ with respect to $U$. We want to understand the positions of $J$ and $M$ and the shapes formed. 2. **Rectangle Setup:** - Rectangle $AUNT$ has vertices $A$ (top-left), $U$ (top-right), $N$ (bottom-right), and $T$ (bottom-left). - Dimensions: $AU=6$ cm (horizontal), $UN=3$ cm (vertical). 3. **Position of Point $J$:** - $J$ lies on the line through $N$ and $T$ but outside the segment $NT$. - Given $TJ = UI$ and $I$ lies on $AU$. - Since $AU=6$ cm, $UI \leq 6$ cm. - Therefore, $TJ = UI \leq 6$ cm. - The segment $NT$ is 6 cm long. - If $J$ were to the right of $N$, $TJ > 6$ cm, which is impossible. - Hence, $J$ lies to the left of $T$ on the extended line. 4. **Position of Point $M$:** - $M$ is symmetric to $N$ with respect to $U$. - Since $UN=3$ cm vertically, $M$ is vertically above $U$ by the same distance. - So, $UM = UN = 3$ cm. - The line $NUM$ is vertical with total length $6$ cm. 5. **Shapes Formed:** - Rectangle $AUNT$ is the base. - Parallelogram $AMUT$ connects $A$, $M$, $U$, and $T$. - Isosceles triangle $AMN$ has base $MN=6$ cm and vertex $A$. - Since $A$ connects to $U$ at a right angle, $AM = AN$. 6. **Summary:** - $J$ is outside the rectangle on the left of $T$ such that $TJ = UI \leq 6$ cm. - $M$ is vertically above $U$ at distance $3$ cm. - The figure forms a step shape with rectangle $AUNT$ and parallelogram $AMUT$ stacked. This completes the detailed explanation of the figure and point placements.