Question
Find the equation of the line that goes through the point (-3, 4) and is perpendicular to the line that passes through (-4, -4) and (-4, 4).
Answers
Answered by
GPT-4o mini
To find the equation of the line that goes through the point \((-3, 4)\) and is perpendicular to the line that passes through the points \((-4, -4)\) and \((-4, 4)\), we first need to determine the slope of the line defined by the two points \((-4, -4)\) and \((-4, 4)\).
The coordinates \((-4, -4)\) and \((-4, 4)\) indicate that both points have the same x-coordinate, which means this line is vertical. The slope of a vertical line is undefined.
A line that is perpendicular to a vertical line must be horizontal. The slope of a horizontal line is \(0\).
Since we have determined the slope of the line we want to find is \(0\) (indicating a horizontal line), we know that all points on this line will have the same y-coordinate as the point \((-3, 4)\), which is \(4\).
Thus, the equation of the line can be expressed as:
\[
y = 4
\]
This is the required equation of the line that passes through the point \((-3, 4)\) and is perpendicular to the vertical line through \((-4, -4)\) and \((-4, 4)\).
The coordinates \((-4, -4)\) and \((-4, 4)\) indicate that both points have the same x-coordinate, which means this line is vertical. The slope of a vertical line is undefined.
A line that is perpendicular to a vertical line must be horizontal. The slope of a horizontal line is \(0\).
Since we have determined the slope of the line we want to find is \(0\) (indicating a horizontal line), we know that all points on this line will have the same y-coordinate as the point \((-3, 4)\), which is \(4\).
Thus, the equation of the line can be expressed as:
\[
y = 4
\]
This is the required equation of the line that passes through the point \((-3, 4)\) and is perpendicular to the vertical line through \((-4, -4)\) and \((-4, 4)\).