# Question #4f42d

Mar 11, 2015

The condition for your line to be perpendicular to the given one is that:
${m}_{1} \cdot {m}_{2} = - 1$
where $m$ is the gradient (or slope) of the line.
Your line CA has slope = ${m}_{1} = \frac{\Delta y}{\Delta x} = \frac{2 - \left(- 3\right)}{- 8 - 7} = - \frac{1}{3}$
So your perpendicular line will have slope ${m}_{2} = 3$.

Now, given the coordinates of a point such as (${x}_{3} , {y}_{3}$), you can determine the equation of a specific line perpendicular to CA as:
$y - {y}_{3} = {m}_{2} \left(x - {x}_{3}\right)$

hope it helps