Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have three points $A=(2,3), B=(6,4)$ and $C=(6,6).$ Given $\vec{AB}=\vec v$ and $\vec{BC}={0 \choose 2}$. I have also that for every $t\in [0,1]$ there is a point $D$ given as $\vec{AD}=t\vec{v}.$

My question is determine $t$ such that the area of triangle $ADC$ equals area of the triangle $DBC$.

My suggestions is Can I say that $D$ is on line $AB$ dividing the area of $ABC$ in to two equal parts, namely $ADC$ and $DBC$? If this is true then why is it true?

Thanks a lot.

share|improve this question

2 Answers 2

Yes, $t=\frac12$. Hint: The triangles $ADC$ and $DBC$ have the same altitude.

share|improve this answer
    
Thanks.njguliyev –  Reader Sep 20 '13 at 19:14

$$\overrightarrow{AD}=t\overrightarrow{v}$$ means that $AD$ and $v$ are linearly dependent. Also we can say $D\in[AB]$ because of $t\in[0,1]$. For $ADC$ and $DBC$ have same areas $t$ must be $1/2$ and hence $D=(4,7/2)$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.