distance of a point from a line

Author:
Mathguru
We can clearly see the graph of line a is shown in red colors and its equation is written in the form ax + by = c. This line passes through two points (blue) B and C. Point A is present on the coordinate plane and its coordinates are (x1, y1). D is the foot of the perpendicular which is drawn from the point A onto the line ‘a’. Length of the line segment DA (green) is equal to the distance of point A from the line ‘a’. We can move these three free points A, B and C and observe how the position of line ‘a’and the length of AD change.
Questions to think about Find the value of |(ax_1+by_1+c)/√(a^2+b^2 )| and compare this with the distance AD, what do we observe?