Perpendicular Lines

L2MAEL

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Perpendicular lines are lines that intersent each other at $90^o$.

To prove this, you can use the equation below:

$$m_1\times m_2=-1$$

$m_1$ is the gradient of the first line, and $m_2$ is the gradient of the second line.

If you don’t want to go through that multiplication, flip your number, and reverse the sign.

For example, if the gradient of line 1 is $2$, the perpendicular gradient could be found by flipping $2$ into $\frac{1}{2}$, and reversing the sign $\left(-\frac{1}{2}\right)$.

$\therefore$ the $\perp$ gradient would be $-\frac{1}{2}$.

Our school required us to write that exact equatio down. Again, other schools may have it differently, so follow your school/classes way of proving.

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Perpendicular Bisector

Now, there is the perpendicular bisector.

A perpendicular bisector is a line that bisects another line at exactly $90^o$. To bisect means to divide into two equal parts.

To put it in simple coordinate geometry terms, it is a perpendicular line passing through the midpoint.

(Finding the midpoint is explained in the other file)