Let `P(0,1)and Q(4,0)` are two points. Find the slope of line perpendicular to PQ.

Answer

To find the slope of the line perpendicular to the line segment connecting the points P(0, 1) and Q(4, 0), we can follow these steps:

### Step 1: Find the slope of line PQ

The formula to find the slope (m) between two points (x1, y1) and (x2, y2) is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, we have:
- Point P (x1, y1) = (0, 1)
- Point Q (x2, y2) = (4, 0)

Substituting the coordinates into the slope formula:

\[ m_{PQ} = \frac{0 - 1}{4 - 0} = \frac{-1}{4} \]

### Step 2: Use the relationship between slopes of perpendicular lines

If the slope of line PQ is \( m_{PQ} \), then the slope of the line perpendicular to it (let's call it \( m_{perpendicular} \)) can be found using the relationship:

\[ m_{PQ} \cdot m_{perpendicular} = -1 \]

Substituting the value of \( m_{PQ} \):

\[ \left(-\frac{1}{4}\right) \cdot m_{perpendicular} = -1 \]

### Step 3: Solve for the slope of the perpendicular line

To find \( m_{perpendicular} \), we can rearrange the equation:

\[ m_{perpendicular} = \frac{-1}{-\frac{1}{4}} = 4 \]

### Conclusion

Thus, the slope of the line perpendicular to the line segment PQ is:

\[ \boxed{4} \]

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