About Perpendicular Line Formula
A straight line across a point is called a perpendicular line. It forms a 90-degree angle with a specific location through which the line passes. Finding the perpendicular line requires knowledge of coordinates and line equations. The slope should be a/b if the equation of the line is axe + by + c = 0 and the coordinates are (x1, y1). The product of slopes should be -1 if one line is perpendicular to this line. Let m1 and m2 be the slopes of two lines, and their product will be -1 if they are perpendicular to each other.
Perpendicular lines = m1m2 = -1
Slope = -a/b
Perpendicular line equation (y-y1) = -m(x-x1)
Solved example of Perpendicular Line Formula
Example: Check whether 2x + 3y + 5 = 0 and 3x – 2y + 1 = 0 are perpendicular or not.
Sol: The given equations of lines are:
- 2x + 3y + 5 = 0 and 3x – 2y + 1 = 0
- To check whether they are perpendicular to each other, find out the slopes of both lines. If the product of their slopes is -1, these lines are perpendicular to each other.
- Slope formula is; m = -a/b and Slope for first line, m1 = -a/b = -2/3
- Slope for second line, m2 = -a/b = -3/-2
- m1m2 = -2/3×-3/-2 = -1
Since the product of the slope is -1, the given lines are perpendicular to each other.
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