Let's **reflect the figure over the line \( y = x - 1 \)** We are given the vertices of the figure as: \( A(3, -2) \), \( B(6, -3) \), \( C(4, -8) \), \( D(3, -6) \). Let's find the reflected points step-by-step: --- ### **Step 1: General Formula for Reflection over \( y = x - 1 \)** To reflect a point \( (x_1, y_1) \) over the line \( y = x - 1 \): 1. **Translate the line to \( y = x \):** - Shift all points up by 1: \( (x_1, y_1+1) \) 2. **Reflect over \( y = x \):** - Swap x and y: \( (y_1+1, x_1) \) 3. **Translate back down by 1:** - Subtract 1 from the new y: \( (y_1+1, x_1-1) \) **So, the image of \( (x_1, y_1) \) is \( (y_1+1, x_1-1) \).** --- ### **Step 2: Apply the Formula to Each Vertex** #### **A(3, -2):** - Reflected: \( (y+1, x-1) = (-2+1, 3-1) = (-1, 2) \) #### **B(6, -3):** - Reflected: \( (y+1, x-1) = (-3+1, 6-1) = (-2, 5) \) #### **C(4, -8):** - Reflected: \( (y+1, x-1) = (-8+1, 4-1) = (-7, 3) \) #### **D(3, -6):** - Reflected: \( (y+1, x-1) = (-6+1, 3-1) = (-5, 2) \) --- ### **Step 3: List the Reflected Points** The vertices of the reflected figure are: \[ \boxed{ (-1,2),\quad (-2,5),\quad (-7,3),\quad (-5,2) } \] --- ### **Final Answer** **The coordinates of the reflected figure over the line \( y = x - 1 \) are:** - \( \boxed{(-1,2),\ (-2,5),\ (-7,3),\ (-5,2)} \)