The point P (5,-3) is one of the two points of trisection of line segment joining the points A(7,-2) and B(1,-5).

Answer

1

Explanation

Let P (5,-3) divides the line segment joining the points A (7,-2) and B (1,-5) in the ratio k : 1 internally.
By section , the coordinate of point P will be
`((k(1)+(1)(7))/(k+1),(k(-5)+1(-2))/(k+1))`
i.e.,`((k+7)/(k+7),(-5k-2)/(k+1))`
Now , `(5,-3)= ((k+7)/(k+1),(5k-2)/(k+1))`
`rArr (k+1)/(k+1)=5`
`rArr k+7=5k+5`
`rArr -4k=-2`
`:.k=(1)/(2)`
So the point P divides the line segment AB in ratio 1 : 2 . Hence , point P in the point of trisection of AB.