How many peprndiculars can be drawn to a given line passing through given point not lying on it ?

Options

A. 0
B. 1
C. 2
D. infinite

Answer

To solve the question "How many perpendiculars can be drawn to a given line passing through a given point not lying on it?", follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to determine how many lines can be drawn that are perpendicular to a given line and pass through a point that is not on that line.

2. **Visualize the Situation**: Draw a horizontal line on your paper. Label it as line AB. Then, choose a point P that is not on line AB.

3. **Draw the Perpendicular**: From point P, draw a line that intersects line AB at a right angle (90 degrees). This line is the perpendicular line from point P to line AB.

4. **Analyze the Perpendicular**: Notice that there is only one unique way to draw a line that is perpendicular to line AB and passes through point P.

5. **Conclusion**: Since only one line can be drawn that meets the criteria of being perpendicular to line AB and passing through point P, the answer is that only one perpendicular can be drawn.

### Final Answer:
Only one perpendicular can be drawn to a given line passing through a point not lying on it.

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