1. The problem asks for the coordinates of triangle XYZ after two transformations: reflection across the y-axis and then translation two units to the right. 2. Reflection across the y-axis changes a point $(x,y)$ to $(-x,y)$. 3. Translation two units to the right changes a point $(x,y)$ to $(x+2,y)$. 4. Given the original points of triangle XYZ are $X(-3,1)$, $Y(-3,4)$, and $Z(0,1)$ (inferred from the options and transformations). 5. Reflect each point across the y-axis: $$X(-3,1) \to X'(3,1),\quad Y(-3,4) \to Y'(3,4),\quad Z(0,1) \to Z'(0,1)$$ 6. Translate each reflected point two units to the right: $$X'(3,1) \to X''(3+2,1) = (5,1),\quad Y'(3,4) \to Y''(3+2,4) = (5,4),\quad Z'(0,1) \to Z''(0+2,1) = (2,1)$$ 7. The final coordinates after both transformations are $X''(5,1)$, $Y''(5,4)$, and $Z''(2,1)$. 8. Comparing with the options, none exactly match these coordinates, but the problem's first question options have points with negative y-values, so let's check the original points from the problem statement. 9. The problem states the original triangle XYZ has vertices $X(1,-6)$, $Y(6,-6)$, and $Z(6,1)$ for the second question, but for the first question, the initial points are not explicitly given. 10. From the position hint, before transformation, the triangle has vertices $X(-5,-1)$, $Y(-5,-4)$, and $Z(-2,-1)$. 11. Reflecting these points across the y-axis: $$X(-5,-1) \to X'(5,-1),\quad Y(-5,-4) \to Y'(5,-4),\quad Z(-2,-1) \to Z'(2,-1)$$ 12. Translating two units to the right: $$X'(5,-1) \to X''(7,-1),\quad Y'(5,-4) \to Y''(7,-4),\quad Z'(2,-1) \to Z''(4,-1)$$ 13. The final coordinates are $X''(7,-1)$, $Y''(7,-4)$, and $Z''(4,-1)$, which corresponds to option D. 14. Therefore, the answer to question 18 is option D. --- 15. For question 19, the original triangle XYZ has vertices $X(1,-6)$, $Y(6,-6)$, and $Z(6,1)$. 16. Reflect across the y-axis: $$X(1,-6) \to X'(-1,-6),\quad Y(6,-6) \to Y'(-6,-6),\quad Z(6,1) \to Z'(-6,1)$$ 17. Translate vertically 4 units (up): $$X'(-1,-6) \to X''(-1,-6+4) = (-1,-2),\quad Y'(-6,-6) \to Y''(-6,-2),\quad Z'(-6,1) \to Z''(-6,5)$$ 18. The final coordinates are $X''(-1,-2)$, $Y''(-6,-2)$, and $Z''(-6,5)$. 19. This completes the transformation for question 19.