检查是否垂直

Remember, perpendicular lines are lines that intersect at a right angle. An interesting property held by perpendicular lines is that the product of the slopes of perpendicular lines multiply equals -1.

Two lines, $\ell$ and $m$, are perpendicular if and only if the angle made between them at their intersection is $90^\circ$.

Two lines, $\ell$ and $m$, are perpendicular if and only if their two-dimensional slopes multiply to $-1$.

If you are given two lines, they are perpendicular if and only if their slopes multiply to be $-1$. If you are given some coordinates, you can use them to find the slopes and check to see if they multiply to $-1$. This is basically all there is to it; you should go on the practice part of this section to see this in action.

Perpendicular lines are lines that intersect once at a $90$ degree angle. The slopes of the two perpendicular lines are the opposite reciprocals of each other. This means that if the slope of one line is $m$ then the slope of the other line is $\frac{-1}{m}$.

The two lines plotted are $y=2x$ (blue) and $y=\frac{-x}{2}$ (green). Because $-(2)^{-1} = \frac{-1}{2}$, the two lines are perpendicular.