Question

Point P (5,-3), one of the two points of trisection of line segment joining the points A (7, - 2) and B (1, - 5)?​

Answer 1

Step-by-step 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. So the point P divides the line segment AB in ratio 1 : 2 . Hence , point P in the point of trisection of AB.

Answer 2

Answer:

Step-by-step explanation:

Answer

Using the section formula, if a point (x,y) divides the line joining the points (x  

1

​

,y  

1

​

) and (x  

2

​

,y  

2

​

) in the ratio m:n, then  

(x,y)=(  

m+n

mx  

2

​

+nx  

1

​

 

​

,  

m+n

my  

2

​

+ny  

1

​

 

​

)

Also, we know that the points of trisection divide the line segment in ratio 2:1 and 1:2

Therefore, the points of trisection of line segment AB are given by

=(  3

2×1+1×7  ,  3

2×−5+1×−2  ) and (  3 1×1+2×7  

,  3 1×−5+2×−2  )

=(  3 9  ,  3 −12  ) and (  3 15   ,  3 −9   )  

=(3,−4) and (5,−3)

Hence, the given statement is true.