To find the equation of line perpendicular to Ax+By+C=0, we use the concept that perpendicular lines have negative reciprocal slopes. This is a key idea in coordinate geometry.
Given
Equation of the given line:
Ax + By + C = 0
Perpendicular Line Concept
The slope of the given line is −A/B.
The slope of any line perpendicular to it will be the negative reciprocal, which is B/A.
Required Equation
Using slope-intercept form, the equation of a line with slope B/A is:
y = (B/A)x + k, where k is constant.
Rearranging to standard form:
Bx − Ay + D = 0 (D is new constant)
Note:
Any line perpendicular to Ax + By + C = 0 can be written in the form Bx − Ay + D = 0, where D is a constant.
Equation of Any Line Perpendicular to Ax + By + C = 0
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