Find the shortest distance between points and the line

To find the shortest distance between a point and a line in a 2D plane, we use the formula:

\[
d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}
\]

Here, the equation of the line is given as:

\[
Ax + By + C = 0
\]

And the coordinates of the point are \( P(x_1, y_1) \).

**Steps:**
1. Identify the coefficients \( A \), \( B \), and \( C \) from the line equation.
2. Plug the coordinates of the point \( (x_1, y_1) \) into the formula.
3. Calculate the absolute value of \( Ax_1 + By_1 + C \).
4. Divide that result by \( \sqrt{A^2 + B^2} \).

Would you like to provide a specific point and line equation so I can calculate the shortest distance?

### 5 Related Questions:
1. What is the shortest distance between two parallel lines?
2. How do you find the equation of a line perpendicular to a given line?
3. How does the formula change in 3D geometry for shortest distance?
4. Can this method be applied to curved lines, like a parabola?
5. What are alternative methods to calculate the distance from a point to a line?

### Tip:
The shortest distance between a point and a line is always along the perpendicular from the point to the line.

Discover how to find the shortest distance between a point and a line using the formula d = |Ax1 + By1 + C| / √(A² + B²). This tutorial explains the step-by-step process to apply the formula and understand the perpendicular distance theorem, ideal for high school students in Grades 9-12.

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