distance in plane the lecture 2 part1

Lecture no 2 part 1

Distance in the plane :


Q(x2-y2)

(y2-y1)

(x2-x1)

P(x1-y1)





Examples : calculate the distance between :
1. (-1,2), (3,4)
2. the origin and (x, y)
3. the radius of a circle has center (h,k) and the point passing through p(x,y).
4. a particle moves from A to B in the coordinate plane find the increments in the particles coordinate also find the distance from A to B .
A (-3,2), B (-1,-2)
A , B( 0, 1.5)
5. describe the graph of the equations
x2+y2=1
x2+y2<3
x2+y2=0

6. find the equation for a. vertical line and b. the horizontal line through the given point:
a. (-1,4/3)
b. (- )
Functions and their graphs :

Functions are the key to describe the real world in mathematical terms.
The area of a circle depends on the radius, the distance an object travels at constant speed from an initial position a long straight line path depends on the elapsed time, so the value of one variable y depend on the value of another variable x so we say y is a function of x.

a rule to calculate the area of a circle from its radius r
So y= f(x) in general ,x independent variable ,y dependent variable .
Definition
Domain : all possible input value
Range : the set of all values of f(x) as x varies through out d is called the range of the function.

Function Domain Range
Y=x2 (- )
[0, )

Y=1/x


Y=
[0, )
[0, )

Y=
( ]
[0, )


Example : graph the function y=x2 over the interval [-2,2]


X=-2, y=4
X=-1, y=1
X=3/2, y=9/4 y=x2