we can take out the slope of a line if we know the coordinates of two points in a plane

Here we have the two points\((-4,5) and (6,-1)\)

slope is given by \(\frac{y2 - y1}{x2 - x1}\)

slope = \(\frac{-1 - 5}{6- (-4)}\) = \(\frac{-3}{5}\)

Hence option A is correct

For two perpendicular lines there slope should multiply to \(-1\)

For one line we have a slope i.e already -ve so the slope of the second line cannot be negative or else they will multiply to a +ve number

Hence option B is incorrect

Also we know that line k passes through the midpoint of line L

Use the mid-point formula to get \(x = \frac{x1+x2}{2},y=\frac{y1+y2}{2}\)

\(\frac{-4 + 6}{2},\frac{5+ -1}{2}\)

This simplifies to \((1,2)\)

Hence option C is correct

_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes