Mathematics
Shaniyamarie
2016-04-16 07:27:36
Find the point P along the directed line segment from point A(-8,-3) to point B(6,12) that divides the segment in the ratio 1 to 7
ANSWERS
sober919
2016-04-16 10:36:16

bearing in mind that, the ratio here is 1:7 form A to B, that matters, because, the AB segment gets split in 8 pieces, and AP takes 1 slice whilst PB takes 7 slices [latex]f left. qquad ight. extit{internal division of a line segment} \\\ A(-8,-3)qquad B(6,12)qquad ratio1=1qquad ratio2=7qquad 1:7 \\\ cfrac{AP}{PB} = cfrac{1}{7}implies cfrac{A}{B} = cfrac{1}{7}implies 7cdot A=1cdot B \\\ 7(-8,-3)=1(6,12)\\ -------------------------------\\[/latex] [latex]f { P=left(cfrac{ extit{sum of "x" values}}{ratio1+ratio2}quad ,quad cfrac{ extit{sum of "y" values}}{ratio1+ratio2} ight)}\\ -------------------------------\\ P=left(cfrac{(7cdot -8)+(1cdot 6)}{1+7}quad ,quad cfrac{(7cdot -3)+(1cdot 12)}{1+7} ight)[/latex]

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