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I hope it's enough understandable.

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3 Answers 3

up vote 1 down vote accepted

Hint: consider the slope of the line, using the different points.

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There are many approaches, and which one is best depends on your background knowledge. One that I like is the fact that if we treat points as vectors, then the points $W$ on the line segment joining $A$ and $B$ have the shape $$W=(1-t)A+tB,$$ where $0 \le t \le 1$. Moreover, the distance of $W$ from $A$ is $t$ times the distance of $B$ from $A$.

In our case, we have $A=(a,9)$, $B=(8,-3)$, $W=(2,v)$, and $t=1/3$. So we get $$(2,v)=\frac{2}{3}(a,9)+\frac{1}{3}(8,-3).$$ That tells us that $2=\frac{2}{3}a +\frac{1}{3}(8)$ and $v=\frac{2}{3}(9)+\frac{1}{3}(-3)$.

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You can use the Inner Point Formula too, in order to find the points. http://www.teacherschoice.com.au/Maths_Library/Analytical%20Geometry/AnalGeom_3.htm

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This could be explained more fully so that it is helpful. –  rschwieb Oct 12 '12 at 16:40
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