Question

Question 9
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

True
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 formula, the coordinate of point P will be
$(\frac{k\left(1\right)+\left(1\right)\left(7\right)}{k+1},\frac{k(-5)+1(-2)}{k+1})i.e.,(\frac{k+7}{k+1},\frac{-5k-2}{k+1})Now,(5,-3)=(\frac{k+7}{k+1},\frac{-5k-2}{k+1})\Rightarrow \frac{k+7}{k+1}=55k+5=k+7\Rightarrow -4k=-2\therefore k=\frac{1}{2}$
So the point P divides the line segment AB in ratio 1:2.
Hence, point P in the point of trisection of AB.