To find the equations for Runway B (parallel to Runway A) and Runway C (perpendicular to Runway A), we first need the slope of Runway A, which is not provided in the question. For the sake of explanation, let's say the equation for Runway A is given in slope-intercept form as \(y = mx + b\), where \(m\) is the slope.
Runway B (Parallel to Runway A):
Since Runway B is parallel to Runway A, it will have the same slope \(m\). The general form of the equation for Runway B can then be written as: \[ y = mx + b' \] To ensure it passes through the point (0, -4), we can find \(b'\): \[ -4 = m(0) + b' \implies b' = -4 \] Thus, the equation for Runway B can be expressed as: \[ y = mx - 4 \]
Runway C (Perpendicular to Runway A):
For Runway C, which is perpendicular to Runway A, its slope will be the negative reciprocal of \(m\), denoted as \(-\frac{1}{m}\). The equation can be constructed similarly to Runway B: \[ y = -\frac{1}{m}x + b'' \] To ensure it passes through the point (0, -4), we can determine \(b''\): \[ -4 = -\frac{1}{m}(0) + b'' \implies b'' = -4 \] Therefore, the equation for Runway C can be written as: \[ y = -\frac{1}{m}x - 4 \]
In conclusion, the equations for both Runway B and Runway C, assuming \(m\) is the slope of Runway A, are:
- For Runway B: \(y = mx - 4\)
- For Runway C: \(y = -\frac{1}{m}x - 4\)
Please note: To provide explicit equations, we would need the slope of Runway A or its equation. You should substitute the proper value of \(m\) based on the actual slope of Runway A if you are applying this in a specific context. If the equation of Runway A is provided, let me know, and I can refine these equations further!
2 answers