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  • 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).

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).

Answers (1)

Answer.       [True]
Solution.        
                
Let the two point of trisection are C, D
Point \, \, C= \left ( \frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}} ,\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}\right )
(x1, y1) = (7, -2)           (x2, y2) = (1, -5)
m1 = 1 , m2 = 2    (Because C divide AB in ratio 1:2 )
C=\left ( \frac{1\times 1+2\times 7}{1+2} ,\frac{1\times -5+2\times -2}{1+2}\right )
C= \left ( \frac{1+14}{3} ,\frac{-5-4}{3}\right )
C= \left ( 5,- 3 \right )
Point \, \, D= \left ( \frac{n_{1}x_{2}+n_{2}x_{1}}{n_{1}+n_{2}} ,\frac{n_{1}y_{2}+n_{2}y_{1}}{n_{1}+n_{2}}\right )
n1 = 2 , n2 = 1    (Because D divide AB in ratio 2:1)
D=\left ( \frac{2\times 1+1\times 7}{2+1} ,\frac{2\times -5+1\times -2}{2+1}\right )
D=\left ( \frac{2+7}{3},\frac{-10-2}{3} \right )
D=\left ( 3,-4 \right )
Hence, the given statement is true.

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