The Basic Concepts of lines and Angles
Two points in space define a line
Only one line pass through these 2 points. A line has
infinite number of points.
An angle is the union of two rays with a common end point. The sides of
the angles are the two rays, while the vertex is their common endpoint. An
angle is represented by Ð and three letters. The first and third letters
represent points on each of the rays that form one of the sides. The
middle letter represents the vertex. The first and last letters are
interchangeable. ÐABC and ÐCBA represent the same angle. Since B is the
vertex, it is always in the middle of the two letters.
Co-ordinate Geometry
Coordinates are pairs of numbers that are used to determine points in a
plane, relative to a special point called the origin. The origin has
coordinates (0, 0).
The two axes X’OX and Y’OY divide the plane into four regions called
the quadrants. The ray OX is taken as positive x-axis, OX’ as negative x
axis, OY as positive y-axis and OY’ as negative y-axis. The following
signs of abscissa and ordinate thus characterize the quadrants:
I. Quadrant x > 0, y > 0 or (+,+) II.
Quadrant x < 0, y > 0 or (–,+)
III. Quadrant x < 0, y < 0 or (–,–) IV. Quadrant x > 0, y
< 0 or (+,–)
Distance Formula
Let P(x1, y1) and Q(x2, y2) be any two points on the plane, then the
distance between P and Q is given by
Relationship between three points (Section Formula)
If P is a point dividing the joint of two points A(x1, y1) and B(x2,
y2) internally in the ratio m : n (i.e. PA : PB = m : n) then the
co-ordinates (x, y) of P are given by
If P(x, y) divides the joint of A(x1, y1) and B(x2, y2)
externally in the ratio m : n (i.e. PA : PB = m : n) then the co-ordinates
(x, y) of P are given by
If P is the midpoint of AB, then m = n, and the ratio is 1 :
1. The coordinates of the midpoint of the line segment joining A(x1, y1)
and B(x2, y2) is
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