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

[size=150]What do we mean by distance of a point from a line or distance of a point to a line?[/size]
Distance of a Point to a Line
Exploration
[size=150]What is the distance of point [i]A[/i] (4, 4) to the line [i]CD[/i] (or distance of point[i] A[/i] from the line [i]CD[/i])?[br]Is it the same as the length of the line segment [i]AB[/i][br]What is the length of the line segment [i]AB ?[/i][/size]
[size=150]If we move point [i]B[/i] on the line [i]CD[/i], is the length [i]AB[/i] now changed?[/size]
[size=150]Is there a particular distance that is the shortest between point [i]A [/i]at (4, 4) and the line [i]CD[/i]? [br][/size][size=150]Keep moving point [i]B[/i] until you find the shortest distance. What is the shortest distance ?[/size]
[size=150]What is the angle between [i]AB [/i]and [i]CD[/i] when the shortest distance of [i]AB[/i] is achieved?[/size]
[size=150]Now shift point [i]A [/i]to (7, 5). What is the distance of point [i]A[/i] from the line [i]CD[/i] , using the distance [i]AB [/i]now?[/size]
[size=150]Move point [i]B [/i]on the line [i]CD[/i] again. Has the distance of the point [i]B[/i] from the line [i]CD[/i] changed?[/size]
[size=150]Is there a particular distance that is shortest between point [i]A[/i] at (7, 5) and the line [i]CD[/i]?[br][/size][size=150]What is the shortest distance between [i]A [/i]and the line [i]CD[/i]?[/size]
[size=150]What is the angle between[i] AB[/i] and[i] CD[/i] when this occurs?[/size]
[size=150][u][b]Conclusion[/b][/u][br][br]What can we say about the distance of a point A to a line (or distance of a point from a line) ?[br][/size]
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– Lew W. S., John Rodgers

Information: Distance of a Point from a Line (of a point to a line)