(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)
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 \(\color{brown}\boxed{-1}\)