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

[size=150]What do we mean when we say :[br]1. Find the shortest distance of a point from a line ? or [br]2. Find the distance of a point to a line ?[br][br]They are asking for the same distance. But do you know what that means. [br]Explore the activity below to understand the concept and meaning. [/size]
Distance of a Point to a Line
Exploration
[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 the 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 distance that is the shortest between point [i]A [/i]at (7, 6) and the line [i]CD[/i]? [br][/size][size=150]Keep [b]dragging [color=#ff0000]point [/color][i][color=#ff0000]B[/color] [/i][/b] 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 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]
Zamknij
– Lew W. S., John Rodgers

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