1. **Problem statement:** We need to determine if the diagonals AC and BD of quadrilateral ABCD are perpendicular. 2. **Key concept:** Two lines are perpendicular if the product of their slopes is $-1$. 3. **Step 1: Find the slopes of AC and BD.** - Suppose the coordinates of points A, B, C, and D are known or given as $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$, and $D(x_4,y_4)$. - The slope of AC is given by: $$m_{AC} = \frac{y_3 - y_1}{x_3 - x_1}$$ - The slope of BD is given by: $$m_{BD} = \frac{y_4 - y_2}{x_4 - x_2}$$ 4. **Step 2: Check the product of slopes:** Calculate: $$m_{AC} \times m_{BD}$$ If this product equals $-1$, then AC is perpendicular to BD. 5. **Step 3: Conclusion:** - If $m_{AC} \times m_{BD} = -1$, then AC is perpendicular to BD. - Otherwise, they are not perpendicular. **Note:** Without the coordinates of points A, B, C, and D, we cannot numerically verify perpendicularity. You need to provide the coordinates or additional information to proceed with calculations.