1. The problem involves performing dilations on points or shapes with given centers and scale factors $k$. 2. The dilation formula for a point $P(x,y)$ with center $C(x_c,y_c)$ and scale factor $k$ is: $$P'(x',y') = (x_c + k(x - x_c), y_c + k(y - y_c))$$ This means you multiply the vector from the center to the point by $k$ and add it back to the center coordinates. 3. For each problem: - Identify the center $C$ and scale factor $k$. - Apply the formula to each point if given. - For percentages, convert to decimal (e.g., 75% = 0.75, 120% = 1.2). - Negative $k$ means dilation with reflection through the center. 4. Example for problem 7: Points $X(6,-1)$, $Y(-2,-4)$, $Z(1,2)$, $k=3$, center not explicitly given, assume origin or specified center. 5. For problem 8: Points $A(0,5)$, $B(-10,-5)$, $C(5,-5)$, $k=120\% = 1.2$, center $C$. Apply formula: $$A' = (5 + 1.2(0-5), -5 + 1.2(5+5)) = (5 - 6, -5 + 12) = (-1,7)$$ Similarly for $B'$ and $C'$. 6. For problem 12: Points $R(-7,-1)$, $S(2,5)$, $T(-2,-3)$, $U(-3,-3)$, $k=-4$, center $R$. Calculate $S'$: $$x' = -7 + (-4)(2 + 7) = -7 - 36 = -43$$ $$y' = -1 + (-4)(5 + 1) = -1 - 24 = -25$$ 7. The graph description indicates a dilation centered at $C$ with segments labeled 28 and 14, showing the scale factor $k=\frac{14}{28} = 0.5$ or similar. 8. Summary: Use the dilation formula for each point with given centers and scale factors, convert percentages to decimals, and apply negative scale factors carefully. Final answers depend on each specific problem's points and centers.