Question

The location of runway A for a new airport is shown on the coordinate plane below.



Two additional runways are planned. Each will pass through the point (0,-4) on the coordinate plane.

Runway B is to be parallel to runway A.

Runway C is to be perpendicular to runway A.

Which equations could describe either of those runways?

Answer 1

To provide the equations for Runway B and Runway C, we first need to determine the slope of Runway A. Since the details about Runway A's coordinates are not provided, let’s assume the equation of Runway A is in the slope-intercept form, \(y = mx + b\), where \(m\) is the slope.

1. **Runway B (parallel to Runway A)**:
- Since Runway B is parallel to Runway A, it will have the same slope as Runway A. The equation can be written in the slope-intercept form, where the y-intercept will be different, and it will still pass through the point (0, -4).
- Given a slope \(m\), the equation of Runway B can be expressed as:
\[
y = mx - 4
\]
- You could also express it in point-slope form as:
\[
y + 4 = m(x - 0) \quad \text{or} \quad y + 4 = mx
\]

2. **Runway C (perpendicular to Runway A)**:
- The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, if the slope of Runway A is \(m\), the slope of Runway C would be \(-\frac{1}{m}\).
- Like Runway B, Runway C should also pass through the point (0, -4). Therefore, its equation can be expressed in slope-intercept form:
\[
y = -\frac{1}{m}x - 4
\]
- In point-slope form, it can be expressed as:
\[
y + 4 = -\frac{1}{m}(x - 0) \quad \text{or} \quad y + 4 = -\frac{1}{m}x
\]

Without the explicit slope from Runway A, we cannot provide exact numeric equations, but the general forms for Runway B and Runway C are outlined above based on the slope \(m\) of Runway A.