Origin is the orthocentre of the triangle formed by the points (5,- 1), (-2,3) and (- 4, - 7) then its ninepoint cente is

A(5, - 1), B(- 2,3), C(- 4,-7).
Orthocentre H = (0, 0). Centroid G = $\left(\frac{5-2-4}{3},\frac{-1+3-7}{3}\right)=\left(\frac{-1}{3},\frac{-5}{3}\right)$
Ninepoint centre N divides HG in the ratio 3 : 1.
$\therefore \mathrm{N}=\left(\frac{3(-1/3)+1\left(0\right)}{3+1},\frac{3(-5/3+1(0)}{3+1}\right)=\left(-\frac{1}{4},-\frac{5}{4}\right)$