|
|
|
|
Learning Analytical/Coordinate/Cartesian Geometry
...from page 7
Projection?
Projection here means "The representation of a figure or solid on a plane as it would look from a particular direction".
Projection of a Point on a Line
The projection of a point
- Not Belonging to the Line
The projection of a point on a line when it is external to the line i.e. a point not belonging to the line is "A point that represents the foot of the perpendicular drawn from the point to the line".
The same point may have different projections on different lines.
| Eg: |
(a) |
The Projection of the point "P" on line l is the point "M"
[The foot of the perpendicular from "P" to the line l] |
|
(b) |
The Projection of the point "P" on line m is the point "N"
[The foot of the perpendicular from "P" to the line m] |
- Belonging to the Line
The projection of a on a line when it is on the line i.e. a point belonging to the line is "The Point itself".
| Eg: |
(a) |
The Projection of the point "A" on line n is the point "A" itself. |
Projection of a Line Segment on a Line
The projection of a line segment on a line is the Line Segment formed by the projections of the end points of the line segment on the line.
The projection of a line segment
- When one end of the line segment lies on the line
| Eg: |
(a) |
 |
is a line segment and l a line, such that "Q" ∈ l and "P" does not. |
| The "Projection of Point "P" on l is "M" and that of "Q" on l is "Q" itself. |
| ⇒ The "Projection of |
|
on l is |
 |
|
|
- When the points of the line segment do not belong to the line
| Eg: |
(a) |
 |
is a line segment and l a line, such that "A" and "B" do not ∈ l. |
| The "Projection of Point "A" on l is "N" and that of "B" on l is "K". |
| ⇒ The "Projection of |
|
on l is |
 |
|
|
|
|
Copyright © Krishbhavara. All rights reserved ♣ Site optimized for Internet Explorer 5.5 and above
