The equation of a line passing through the point , and perpendicular to line joining the points and is .
Further explanation:
The equation of the line passing through point and is as follows:
……(1)
The given line passing through the points and .
Consider the point as and as .
Substitute 4 for , 1 for , -4 for and -3 for in equation (1).
The point slope form of the equation passing through point is as follows:
……(2)
Here, is the slope of the line.
Compare the equation (2) with to obtain the slope of line.
Thus, the slope of the first line is .
The slope of the other line perpendicular to first line is obtained as follows:
……(3)
Substitute for in equation (3).
Since, the second line passing through point , therefore, the equation of the second line is obtained as follows:
Substitute -4 for , 3 for and -2 for in equation (2).
Thus, the equation of the line passing through point and perpendicular to line is .
The graph is attached below in figure 1.
Learn more:
1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
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3. what are the domain and range of the function f(x) = 3x + 5?
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Answer Details :
Grade: Junior high School.
Subject: Mathematics.
Chapter: Coordinate geometry.
Keywords:
lines, straight lines, (4,1),function, point slope, equation of line passing, perpendicular line, graph, domain, intervals, intercepts, function value, intercepts of lines, slope, slope intercept form, continuous, range, point, line segment.