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標題:

Centroid

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• 想入LSE
• VIVIENNE WESTWOOD 價錢@1@
• harry potter msn 閃字@1@

 

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Find the centroid of the quadrilateral A(1,1), B(6, 2), C(8, 6) and D(4, 5).

最佳解答:

Find the centroid of the quadrilateral: A(1,1),B(6, 2),C(8, 6),D(4, 5).centroid(ABD)=(A+B+D)/3=[(1,1)+(6,2)+(4,5)]/3=(1+6+4,1+2+5)/3=(11,8)/3Area(ABD)=|1 6 4 1| |1 2 5 1|/2=(2+30+4-6-8-5)/2=(36-19)/2=17/2=8.5centroid(BCD)=(C+B+D)/3=[(8,6)+(6,2)+(4,5)]/3=(8+6+4,6+2+5)/3=(18,13)/3=(6,13/3)Area(CBD)=|8 6 4 8| |6 2 5 6|/2=|16+30+24-36-8-40|/2=|70-84|/2=7Total=8.5+7=15.515.5*Xbar=8.5*x1+7*x2Xbar=(8.5*11/3+7*6)/15.5=73.1667/15.5=4.72Ybar=(8.5*y1+7*y2)/15.5=(8.5*8/3+7*13/3)/15.5=3.42So Centroid=(4.72, 3.42)......ans

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