To find the slope of a line that is perpendicular to another line, we can use a simple rule from geometry regarding slopes. If the slope of the original line is denoted as m, then the slope of a line that is perpendicular (at a right angle) to it is given by the negative reciprocal of m.
This means that you calculate the negative reciprocal by taking the following steps:
- Reciprocal: First, you find the reciprocal of m, which is 1/m.
- Negative: Next, you take the negative of that value. Therefore, the slope (mperpendicular) of the line that is perpendicular to the original line can be expressed as:
mperpendicular = -1/m
For example, if the slope m of the original line is 2, then the slope of the perpendicular line would be:
mperpendicular = -1/2
Similarly, if the slope m is -3, the slope of the perpendicular line would be:
mperpendicular = 1/3
In summary, to find the slope of a line that is perpendicular to a line with slope m, simply use the formula mperpendicular = -1/m. This relationship is crucial in understanding how different lines interact in a Cartesian plane.