'09 TMSCA #9

[nsguy1350]

19. The coordinates of the vertices of ABC are (-3,-5), (4,6) and (2,-3). The coordinates of the incenter are (a,b). Find b.
B. -1.9
Still having trouble with all triangle centers besides centroid... Help please!
40. The vertices of a quadrilateral are (-6,-3), (4,8), (3,-5) and (-3,2). Find the area.
B. 68

Did 55, missed 0, skipped 5 for a total of 330, +1 for 100% accuracy (TMSCA rule, correct?) for a total of 331, highest score ever! :D

[Salvadoramerican]

finding the area of a quadrilateral in my mind is faster by splitting it into two traingles and using matrices to find the areas of the two triangles

the coordinate of the incenter is (ax1+bx2+cx3)/(a+b+c) , (ay1+by2+cy3)/(a+b+c) where a,b,c are the length of the sides with coordinates

[nsguy1350]

Thanks again! I stil don't know orthocenter or circumcenter though, and when you split the quadrilateral, you split by opposite points correct? Well, of course, but, how do you use matrices to find the area?

[Salvadoramerican]

All you hve to do is
x1 y1 1

x2 y2 1

x3 y3 1

for both triangles, then find each their determinent and divide by positive or negative halve, to me its faster because you just plug, divide and add
Ironically i learn this in my construction technology class last year when we were plotting out floor framing and figuring area