How do you measure the distance between a point and a line?

Question

anonymous · Answer

It is given by:

Suppose the line given is $ax + by + c = 0$ and the point is $(x_1, y_1)$, then :

$$Distance = \frac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}$$

anonymous · Answer

first, find the equation of the line perpendicular to the given line through the given point.

next, find the point of intersection of these two lines

finally, calculate the distance between this point, and the given point.

The above equation is good and will work, but if you need to show work appropriate for the level of the class, you might also want to know the motivation behind the formula.

primeralph · Answer

a point and a line? there are infinite distances..............but if you meant the shortest distance, that's another thing.............