Analytical Geometry
By: Mustafa El Daghaili

The midpoint is the middle
point between two graphed
points

How to calculate the Midpoint

the first thing you need to
calculate Midpoint is the
coordinates of the two points
you want the mid for

lets say you want to calculate
the midpoint of point A (-2,-4)
and point B (6,10)

what you would have to do is
take the X's add them both
then divide them by 2 to find
find the middle. you would also
have to do the same thing for
the Y's

it should look something like
([{x1+x2}/2], [{y1+y2}/2]
This is the formula for Midpoint
plug in the numbers for the points
([{-2+6}/2],[{-4+10}/2])
add the numbers
([{4}/2],[{6}/2)
complete the divisions and you get
the result:
(2,3)

The median is a line that passes
through a vertex and the midpoint
on the other side

Finding the median has to be done
inside a shape of some sort.

let's say you have a triangle with
points at:
A (2,5)
B(4,-1)
C(-2,-5)
how would you fins the median

first you would need to find
the midpoint. for the example
we'll find the midpoint between
A and B.

so:
([{2+4}/2],{5+ -1}/1])
complete the addition
([{6}/2],{4}/2]
divide the results to get
the midpoint
(3,2) is the midpoint

what you have to do now is
calculate the slope of the median
the way you do this is by taking
the midpoint and the vertex that
the median will pass through and
put them in the formula:
y2-y1/x2-x1

it does not matter which Y or
which X is Y1 Y2or X1 X2

for our case, our mid point will be
passing through point C (-2,-5)
therefore the formula with the
numbers will look like:
-5-2/-2-3
= 7/5
(the negatives are disregarded
because a negative and a negative
makes a positive)

now that you have the slope,
you use that along with the
y value and x value and plug
them into the Y=MX+B formula
using the C coordinates, we will
solve for B

y=y-intercept
m=slope
x=x-intercept
B=line elevation from X

-5=7/5(-2)+B
multiply 7/5 by-2
-5=-14/5+B
isolate B
B=-5+14/5
in order to add -5 to 14/5
you need to put -5 into a
fraction. so 5X5=25/5
now we have
B=-25/5+14/5=-11/5

Being that you have fount "B"
you now have everything you
need to know about the median

the median line equation is
y=7/5 X - 11/5

we will be working on the equation
of a circle, ones that have centers
and the origin point of (0,0)

formula to remember: R2 = Y2 + X2
we will be using this formula to calculate
the radius of circles

the 2 after Y2 R2 and X2 represent
the squared symbol

let's say for example you have a circle
that has a point on the circumference
of the circle at point (6,9), here's how
you would figure out the radius

since X2 + Y2 = R2
then all you have to do is plug in the
Y and X coordinates
6(2) +9(2)= R2
36+81=117
now that you have R2 you need to find
the square root of R2 to have found the
radius. so
the square root of 117 = 10.817
10.817 is the radius of the circle