Find the distance from P to l. Line l contains point (-2,1) and (4,1). Point P had coordinates (5,7).

To find the distance from point \( P(5,7) \) to the line \( l \), which contains the points \( (-2, 1) \) and \( (4, 1) \), follow these steps:

### Step 1: Equation of the line \( l \)
The points \( (-2, 1) \) and \( (4, 1) \) show that both have the same y-coordinate (1). This means that the line is horizontal, and the equation of the line is:
\[
y = 1
\]

### Step 2: Distance from point \( P(5,7) \) to the line \( l: y = 1 \)
For a horizontal line \( y = c \), the distance from a point \( P(x_1, y_1) \) to the line is simply the vertical distance between the point and the line. This is given by the absolute difference between the y-coordinates of the point and the line:
\[
d = |y_1 - c|
\]
Here, \( y_1 = 7 \) (from point P) and \( c = 1 \) (from the line equation). Substituting these values:
\[
d = |7 - 1| = 6
\]

Thus, the distance from point \( P(5,7) \) to the line \( y = 1 \) is 6 units.

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Would you like further details on this? Here are some related questions you might find interesting:

1. How do you find the distance from a point to a slanted line?
2. What is the equation of a vertical line passing through given points?
3. How do you calculate the perpendicular distance between two parallel lines?
4. Can the distance between a point and a line ever be negative?
5. How can the distance between two points in 3D space be calculated?

**Tip**: For vertical and horizontal lines, distance calculations become significantly easier as they involve just subtracting coordinates.

Learn how to calculate the distance from point P(5,7) to the line passing through (-2,1) and (4,1). This geometry problem explains the formula for finding the distance between a point and a horizontal line, covering key concepts for students in Grades 6-8.

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