HOW CAN YOU DETERMINE IT TWO LINES ARE PERPENDICULAR?
To determine if two lines are perpendicular, you can follow these steps:
1. Obtain the equations of the two lines in the slope-intercept form (y = mx + c), where 'm' is the slope and 'c' is the y-intercept of each line.
2. Compare the slopes of the two lines. Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is 'm1', the slope of the other line should be (-1/m1).
3. Calculate the slopes of the lines and verify if they are negative reciprocals. If the slopes are indeed negative reciprocals, the lines are perpendicular.
For example, let's say we have two lines with equations y = 2x + 3 and y = -(1/2)x + 4.
The slope of the first line is 2, and the slope of the second line is -1/2. These slopes are indeed negative reciprocals, so the lines are perpendicular.
Remember that this method applies to lines in a two-dimensional Euclidean plane. In higher dimensions or non-Euclidean geometries, different methods may be necessary to determine perpendicularity.