1. The problem asks to find the original points A and B before the transformations given the transformed points A' and B'. 2. The transformations applied are: - Horizontal stretch by $\frac{5}{2}$ and shift 11 to the right. - Vertical stretch by $\frac{7}{8}$ and shift 17 down. 3. The transformation formula given is: $$ (x', y') = \left( \frac{x}{b} + h, ay + k \right) $$ where $b = \frac{5}{2}$, $h = 11$, $a = \frac{7}{8}$, and $k = -17$ (since shifted down 17). 4. To reverse the transformations (find original points), we reverse the order and operations: - First, undo the horizontal shift: $x' - h$ - Then undo the horizontal stretch: multiply by $b$ - Similarly for vertical: undo vertical shift $y' - k$, then undo vertical stretch by dividing by $a$. 5. Applying this to point A': $$ x_A = b(x'_A - h) = \frac{5}{2}(12 - 11) = \frac{5}{2} \times 1 = \frac{5}{2} = 2.5 $$ $$ y_A = \frac{y'_A - k}{a} = \frac{17 - (-17)}{\frac{7}{8}} = \frac{34}{\frac{7}{8}} = 34 \times \frac{8}{7} = \frac{272}{7} \approx 38.857 $$ 6. Applying this to point B': $$ x_B = b(x'_B - h) = \frac{5}{2}(16 - 11) = \frac{5}{2} \times 5 = \frac{25}{2} = 12.5 $$ $$ y_B = \frac{y'_B - k}{a} = \frac{23 - (-17)}{\frac{7}{8}} = \frac{40}{\frac{7}{8}} = 40 \times \frac{8}{7} = \frac{320}{7} \approx 45.714 $$ 7. So the original points are approximately: $$ A = (2.5, 38.857), \quad B = (12.5, 45.714) $$ 8. For part d), the problem asks to show that the inverse transformation formula: $$ (x, y) = \left(b(x' - h), \frac{y' - k}{a}\right) $$ follows logically from the forward transformation: $$ x' = \frac{x}{b} + h, \quad y' = ay + k $$ 9. Starting from the forward equations: $$ x' = \frac{x}{b} + h \implies x' - h = \frac{x}{b} \implies x = b(x' - h) $$ $$ y' = ay + k \implies y' - k = ay \implies y = \frac{y' - k}{a} $$ 10. This confirms the inverse transformation formula. 11. Your reverse transformations in part c) are correct if you apply the inverse operations in the order of undoing shifts first, then stretches. 12. Part d) is asking you to algebraically prove the inverse formula from the forward transformation equations.