What is the equation of the line that is perpendicular to the given line and passes through the point $(2,6)$?
x=2
x=6
y=2
y=6
Answer (2)
Recognize that the line x = 2 is a vertical line.
Understand that a line perpendicular to a vertical line is a horizontal line.
Use the point ( 2 , 6 ) to determine the equation of the horizontal line.
Conclude that the equation of the line is y = 6 .
Explanation
Identify the type of the given line and the perpendicular line. The given line is x = 2 . This is a vertical line. A line perpendicular to a vertical line is a horizontal line.
Determine the equation of the horizontal line. A horizontal line has the equation y = c for some constant c . Since the line passes through the point ( 2 , 6 ) , the y -coordinate of the point must satisfy the equation of the line.
State the equation of the line. Therefore, the equation of the line is y = 6 .
Examples
Imagine you're drawing a coordinate plane on a piece of paper. The line x = 2 is a vertical line. Now, you want to draw a line that is perfectly horizontal and crosses the vertical line at the point where y is 6. This horizontal line represents the equation y = 6 . This concept is useful in various fields like architecture, where you need to ensure walls are perpendicular to the floor, or in navigation, where you need to plot routes perpendicular to certain landmarks.
The equation of the line that is perpendicular to the given line x = 2 and passes through the point ( 2 , 6 ) is y = 6 . This represents a horizontal line. Therefore, the answer is y = 6 .
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