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(1,7), (13,-16) and (5,k) are the vertices of a triangle. What is the sum of all possible values of "k" for which the area of the triangle is minimum? (k can only be an integer)

 Jun 11, 2022
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The equation of the line in point-slope form is: \(y - 7 =-\frac{23}{12}\left(x-1\right)\)

 

Now, plugging in \(x = 5\), we find \(y = -{2 \over 3}\).

 

This means when \(k = -{2 \over 3}\), the point form a straight line, so we naturally want k to be the closest integer to \(-{2 \over 3}\), which is \(\color{brown}\boxed{-1}\)

 Jun 11, 2022

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