Final answer:
To find the distance between point P and line L, we can use the formula for the distance between a point and a line. The distance is the absolute difference between the x-coordinate of the point and the x-coordinate of the line.
Step-by-step explanation:
To find the distance between point P and line L, we can use the formula for the distance between a point and a line. First, we need to find the equation of line L. Since the line passes through the points (4, -1) and (4, 9), the x-coordinate of both points is 4, which means the line is vertical and its equation is x = 4. Now we can substitute the coordinates of point P (1, 6) into the equation of line L to find the distance between them.
To substitute the coordinates of point P into the equation x = 4, we can see that the x-coordinate of point P is not equal to 4. This means that point P is not on the line x = 4. Therefore, the distance between point P and line L is the distance between point P and the vertical line x = 4, which is the absolute difference between their x-coordinates: |1 - 4| = 3 units.