Misconceptions about Distance of a Point from a Line (of a point to a line)

What is the distance of point A (7, 6) to the line CD (or distance of point A from the line CD)? Is it the same as the length of line segment AB ? Tick the checkbox Show line segment AB What is the length of the line segment AB ?

If we drag point B along on the line CD, is the length AB now changed?

Is there a particular position on the line CD that we can drag point B to, so that the length AB is shortest possible? Does it happen when point B is at M, the midpoint of line CD? Click on checkbox Show midpoint of segment CD. Drag point B to M. Is length AB is shortest when B is placed at M?

Keep dragging point B until you find the shortest length AB. This will also be the shortest distance between point A and line CD. What is this shortest distance ?

What is the angle between AB and CD when the shortest distance of AB is achieved? (Click on checkbox Show ABC)

Now drag point A to (5, 5). What is the distance of point A from the line CD (using the distance AB)now?

Drag point B on the line CD again. Has the distance of the point B from the line CD changed?

Is there a particular distance that is shortest between point A at (5, 5) and the line CD? What is the shortest distance between A and the line CD?

What is the angle between AB and CD when this occurs?

Conclusion When we ask for the shortest distance of a point (say A) to a line (or distance of a point A from a line) what conditions must be satisfied?