Point P(5, −3) is one of the two points of trisection of the line segment joining the points A (7, −2) and B (1, − 5) near to A. Find the coordinates of the other point of trisection.
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 $\mathrm{Q}=\left(\frac{5+1}{2}, \frac{-3-5}{2}\right)$
$=\left(\frac{6}{2}, \frac{-8}{2}\right)$
$=(3,-4)$
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