How can you determine if two lines are perpendicular?
· How the slopes of two perpendicular lines relate;
· How you recognize if two lines are perpendicular on a graph;
· How you recognize if two lines are perpendicular simply from their equations.
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To determine if two lines are perpendicular, you can consider the following methods:
1. Slopes of Two Perpendicular Lines:
In a coordinate plane, if the slopes of two lines are negative reciprocals of each other, then the lines are perpendicular. The negative reciprocal of a number is obtained by flipping the fraction and changing its sign. So, if the slope of one line is m1, the slope of the other line should be -1/m1 in order for them to be perpendicular. If the slopes are not negative reciprocals of each other, then the lines are not perpendicular.
2. Graphical Method:
On a graph, you can determine if two lines are perpendicular by examining the slopes and the angles they form with the x-axis. If the lines intersect and the angle between them is 90 degrees (a right angle), then they are perpendicular.
3. Equation Method:
If you have the equations of two lines, you can determine if they are perpendicular by comparing their slopes. The standard form of the equation for a line is y = mx + b, where m represents the slope. If the slopes of the two lines are negative reciprocals of each other, then the lines are perpendicular. For example, if one line has the equation y = 2x + 3, and another line has the equation y = -(1/2)x + 5, the slopes are -1/2 and 2, respectively. Since the slopes are negative reciprocals, the lines are perpendicular.
Remember, these methods can be used individually or in combination to determine if two lines are perpendicular.