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In a triangle ABC (figure) the points P and Q are selected in the sides AC and BC respectively in a way that PC is half of BC and QC is half of AC:#bar(PC)/bar(BC) = 1/2; bar(QC)/bar(AC)= 1/2#. Find #bar(PQ)# if the side #bar(Ab)# is 20?

Answer 1

#PQ=10#

Take #P' = 1/2(C+A)# and #Q'=1/2(C+B)# then

#bar(CP') = bar(CQ)# and #bar(CQ')=bar(CP)# and #abs(bar(P'Q')) = abs(bar(PQ))# #bar(P'Q')# is parallel to #bar(AB)# and #bar(AB)/(bar(BC))=bar(P'Q')/(bar(CQ'))=bar(PQ)/(bar(CP))#

Finally #bar(PQ)=bar(CP)/(bar(BC)) xx bar(AB) = 20/2 = 10#

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Answer 2

Sadie Allen

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.