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Elly fat mn 3omry ( 1 – 1 )
Analytic Geometry

 Distance between Two Points

If A ( x 1 , y l ), B ( x 2 , y 2 ) are two points in the coordinate plane then:

2
2
AB = x  x 1    y  y 1  ( Pythagorean theorem ) Y
2
2
B ( x 2 , y 2 )
y 2
y 2 – y 1
y 1 A ( x 1 , y 1 ) 
x 2 – x 1
 The Slope of a Line
X'  X
 O x 1 x 2
The slope of the straight line AB is Y'

y  y
tan  = 2 1
x  x 1
2
Special Case:

 If A ( x, y ) is a point in the coordinate plane, then Y
A ( x, y )
2
OA = x  y 2
y
 y 
 The slope of OA is O x X
x

y
tan  =
x

The coordinates of the mid-point of a straight segment

If A ( x 1 , y 1 ), B ( x 2 , y 2 ) and C ( x, y ) where C in the mid-point of AB , then
x  x y  y
x = 1 2 , y = 1 2
2 2

The area of a triangle given the coordinates of its vertices

The area of the triangle ABC where A ( x 1 , y 1 ) , B ( x 2 , y 2) and C ( x 3 , y 3 ) is given by

x y 1
1 1 1
 ABC = | D | where D = x y 1
2 2 2
x 3 y 3 1

Calculus 10 Unit (1)