Question

find the coordinates of the points of trisection of the line segment joining the points A(1,-2) and B(-3,4)​

Answer 1

A(1,-2) is in fourth quadrant

B(-3,4) is in second quadrant

Answer 2

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we will use this formula $\frac{m_1x_2+m_2x_1}{m_1+m_2}$ , $\frac{m_1y_2+m_2y_1}{m_1+m_2}$

D divides line segment ab into ratio of 1:2

$m_1=1,m_2= 2$ $x_1=1,x_2= -3$ $y_1=-2,y_2= 4$  

D = $\frac{1(-3)+2(1)}{1+2}$ , $\frac{1(4)+2(-2)}{1+2}$

D = $\frac{-3+2 }{3}$ , $\frac{4-4}{3}$

D = $\frac{-1 }{3}$ , $\frac{0}{3}$

D = $\frac{-1 }{3}$ , $0$

D coordinates are $\frac{-1 }{3}$ , $0$

C divides line segment ab into ration of 2:1 $m_1=2,m_2= 1$ $x_1=1,x_2= -3$ $y_1=-2,y_2= 4$  

c = $\frac{2(-3)+1(1)}{1+2}$ , $\frac{2(4)+1(-2)}{1+2}$

c = $\frac{-6+1 }{3}$ , $\frac{8-2}{3}$

c = $\frac{-5 }{3}$ , $\frac{6}{3}$

c = $\frac{-5 }{3}$ , $2$

c coordinates are $\frac{-1 }{3}$ , $2$