To determine the value of $x$ that makes line $BC$ parallel to line $AD$ and perpendicular to line $AB$, we must analyze the geometric relationships. Let’s break it down step by step:

---

1. Understand the problem setup:

• Point $C$: Given as $(x, 2)$.
• Lines involved:
  • Line $BC$: Passes through $B$ and $C$.
  • Line $AD$: Parallel to $BC$.
  • Line $AB$: Perpendicular to $BC$.

2. Slope conditions for parallel and perpendicular lines:

• If two lines are parallel, their slopes are equal: $m_{BC} = m_{AD}$.
• If two lines are perpendicular, the product of their slopes is $-1$: $m_{AB} \cdot m_{BC} = -1$.

---

3. Define points $A$, $B$, and $D$:

Without specific coordinates for $A$, $B$, and $D$, the solution depends on their locations. Could you provide their coordinates or describe their positions? For example:

• Where is point $A$?
• Where is point $B$?
• Where is point $D$?

This information is necessary to compute the slopes of the lines and solve for $x$.

Would you like to clarify the positions of the points? 😊

---

Follow-up Questions:

1. What are the coordinates of points $A$, $B$, and $D$?
2. Are there any additional constraints or conditions for the lines or points?
3. Is the coordinate $x$ in $C(x, 2)$ assumed to be a specific type (e.g., integer)?
4. Do you want the solution presented with general algebra or numerical answers?
5. Would you like a diagram for visualization?

---

Tip:

When solving geometry problems, always clearly define the positions of all points and lines before applying slope or distance formulas.