Analytical Geometry By: Mustafa El Daghaili

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Analytical Geometry By: Mustafa El Daghaili

Equation of a Circle

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

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

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

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

Median

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

this is a visual representation of what we just did

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

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

-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

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

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)

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

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

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

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

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

Midpoint

How to calculate the Midpoint

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)

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

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

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

The midpoint is the middle point between two graphed points