Point P(5, −3) is one of the two points of trisection of the line segment j

We are given a line segment joining points A (7, −2) and B (1, −5)

P (5, −3) is one of the two points of trisection of line segment AB

P is near to A

We are to find the coordinates of other points of trisection

Let the other point of trisection is Q

Therefore

AP = PQ = QB

That is Q is the mid point of line segment PB

We know that the coordinates of mid point of line segment with coordinates of end points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Therefore the coordinates of point $\mathrm{Q}=\left(\frac{5+1}{2}, \frac{-3-5}{2}\right)$

$=\left(\frac{6}{2}, \frac{-8}{2}\right)$

$=(3,-4)$