If the centroid of the triangle formed by the points (3, −5), (−7, 4),

We have to find the unknown co-ordinates.

The co-ordinates of vertices are $\mathrm{A}(3,-5) ; \mathrm{B}(-7,4) ; \mathrm{C}(10,-k)$

The co-ordinate of the centroid is $(k,-1)$

We know that the co-ordinates of the centroid of a triangle whose vertices are $\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right)$ is-

$\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right)$

So,

$(k,-1)=\left(\frac{3-7+10}{3}, \frac{-5+4-k}{3}\right)$

Compare individual terms on both the sides-

$k=2$

So the answer is (c)