# What is the shortest distance from the point (x_1, y_1) to the straight line, Ax + By + C = 0?

## Question:

What is the shortest distance from the point (x{eq}_1 {/eq}, y{eq}_1 {/eq}) to the straight line, Ax + By + C = 0?

## Coordinate Geometry:

The following problem deals with the concept of **Coordinate Geometry**, which was introduced by Rene Descartes. The perpendicular distance is always the shortest distance between any two objects.

## Answer and Explanation:

The perpendicular distance of a point (a,b) from the line kx+ly+m=0 is {eq}\displaystyle \boxed{\mathbf{\frac{|ak+bl+m|}{\sqrt{k^2+l^2}}}} {/eq}

Plugging in the variables, we get

{eq}\displaystyle \begin{align} \text{Shortest distance} &= \frac{Ax_1+By_1+C}{\sqrt{A^2+B^2}} \end{align} {/eq}

Therefore, the shortest distance from the point (x_1, y_1) to the straight line, Ax + By + C = 0 is {eq}\displaystyle \boxed{\mathbf{ \frac{Ax_1+By_1+C}{\sqrt{A^2+B^2}}}} {/eq}.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from FTCE Mathematics 6-12 (026): Practice & Study Guide

Chapter 30 / Lesson 5