Notes

Today's work
1) Orthocentre ----------
2) Centroid ---------Finished (only method 1 - QUICK AND EASY METHOD)
3) Quadrilateral ------------ Finished
4) Triangles ----------Finished
5) Midpoint -------- Finished

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CENTROID :

Step1 : Add all the x co-ordinates - Let the sum be $x
Step 2: Add all the y co-ordinates - Let the sum be $y
Step 3 :Divide $x by 3 = ($x ÷ 3 ) - Let the result(x) be x1
Step 4: Divide $y by 3 = ($y ÷ 3 ) - Let the result(y) be y1
Step 5: So , the answer is (x1 , y1)

(x1 , y1) ==> This is the co-ordinates of the centroid of the triangle.
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QUADRILATERAL:
Let the given vertices be : [ (a ,b) | (c , d) | (e , f) | (g , h) ] // The elements are arranged in (x , y) order
Step1 : Make a table with two fields

__________________________________________________________
| Co-ordinates Relationship |
| |
| --------------------------- |
| | X | Y | |
| --------------------------- |
| | a | b | |
| | c | d | |
| | e | f | |
| | g | h | |
| | a | b | |
| --------------------------- |
| ________________________________________________________ |

Algorithm :

(a * d) - (c * b) = $r1 //result 1
(c * f) - (d * e) = $r2 // result 2
(e * h) - (g * f) = $r3 // result 3
(g * b) - (a * h) = $r4 // result 4

result_1 = |$r1|
result_2 = |$r2|
result_3 = |$r3|
result_4 = |$r4|

Final Area ==>>>

result_1 + result_2 + result_3 + result_4
__________________________________________________
2

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TRIANGLES

Let the given vertices be : [ (a ,b) | (c , d) | (e , f) ] // The elements are arranged in (x , y) order

Let the $hr = [ a ( d - f ) ] + [ c ( f - b ) ] + [ e ( b - d ) ] //hr --> half result
Let k = 2

AREA ==>>> $hr / 2

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MIDPOINT

Let the two end point's co-ordinates be (a , b) and (c , d) //Maintained in (x , y) order

Algorithm :

[(a + c ) / 2 ] + [ (b+ d) / 2 ]

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