[size=150]What is the distance of point [i]A[/i] (7, 6) 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 line segment [i]AB [/i]? [br]Tick the checkbox Show line segment [i]AB[/i][br]What is the length of the line segment [i]AB ?[/i][/size]

[size=150]If we [b]drag [color=#ff0000]point [/color][i][color=#ff0000]B[/color] [/i][/b] along on the line [i]CD[/i], is the length [i]AB[/i] now changed?[/size]

[size=150]Is there a particular position on the line [i]CD [/i] that we can drag [b] [color=#ff0000]point [/color][i][color=#ff0000]B [/color][/i][/b]to, so that the length [i]AB [/i]is shortest possible? Does it happen when [b][color=#ff0000]point [/color][i][color=#ff0000]B [/color][/i][/b] is at [i][b]M[/b], [/i][b]the midpoint of line CD[/b]? [br]Click on checkbox Show midpoint of segment [i]CD.[/i][br]Drag [b][color=#ff0000]point [/color][i][color=#ff0000]B [/color][/i][/b]to [i][b]M[/b][/i]. [br]Is length [i]AB [/i]is shortest when [i][color=#ff0000][b]B[/b][/color][/i] is placed at [i][b]M?[/b][/i][/size]

[size=150][size=150]Keep [b]dragging [color=#ff0000]point [/color][i][color=#ff0000]B[/color] [/i][/b]until you find the shortest length [i][b]AB[/b][/i]. [br]This will also be the shortest distance between point [i][b]A[/b] [/i]and line [i][b]CD[/b][/i].[br]What is this shortest distance ?[/size][br][/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?[br][/size][size=150](Click on checkbox Show [math]\angle[/math][i]ABC)[/i][/size]

[size=150]Now drag [b]point [/b][i][b]A[/b] [/i]to (5, 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][b]Drag [color=#ff0000]point [/color][/b][i][b][color=#ff0000]B[/color][/b] [/i]on the line [i]CD[/i] again. Has the distance of the [color=#ff0000]point [i]B[/i][/color] from the line [i]CD[/i] changed?[/size]

[size=150]Is there a particular [b]distance that is shortest between point [i]A[/i] at (5, 5) and the line [i]CD[/i][/b]?[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]When we ask for the shortest distance of a point (say [i]A[/i]) to a line (or distance of a point [i]A [/i]from a line) what conditions must be satisfied?[br][/size]