Basic coordinate Geometry
October 7, 2009
Still have to add lot of diagrams rest is perfectly done!
This sheets contains notes on basic coordinate geometry which starts with
introduction to coordinate geometry and gets you into points, straightlines,
collinearity, A point-line properties, two line properties, linear combination.
Flow of lectures :
Lecture I : We start with introduction of coordinate geometry, how its
related to algebra or a nice use of algebra for geometry. We study all properties,
structures with respect to when we have a single point, two points (collinear,
non-collinear), three points, we study equation of a line, and its different forms,
Transformations - shift of origin & rotation of coordinates axes
Lecture II : We study structure a line and a point, begin with origin side
of a line, short distance of a point from a line, Foot of perpendicular, image of
a point in a line, And how that is helpful for getting the reflection of a line in
another line.
Lecture III : Study two lines, angle bisector - angle bisector containing
origin, angle bisector of an acute angle, locus
Lecture IV : Linear combination & problem solving to complete the topic.
Lecture V : Problem solving
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CONTENTS
CONTENTS
Contents
1 Motivation
4
2 A point
4
2.1 Polar representation . . . . . . . . . . . . . . . . . . . . . . . . .
4
3 Two points
4
3.1 Distance formula . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
3.2 Section formula . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
3.2.1 External section formula . . . . . . . . . . . . . . . . . . .
5
4 Three points
5
4.1 Three points are Non-collinear
. . . . . . . . . . . . . . . . . . .
5
4.1.1 Area of triangle . . . . . . . . . . . . . . . . . . . . . . . .
6
4.1.2 Points of a Triangle
. . . . . . . . . . . . . . . . . . . . .
6
4.2 Three points are Collinear . . . . . . . . . . . . . . . . . . . . . .
7
5 Equation of a line
8
5.1 Forms of a line equation . . . . . . . . . . . . . . . . . . . . . . .
8
5.1.1
Slope point form . . . . . . . . . . . . . . .