Question

Find the coordinates of the points of trisection of the line segment joining the points $(4,-1)and(-2,-3)$

• A. $(0,\frac{-5}{3})$
• B. $(2,0)$
• C. $(6,0)$
• D. $(2,7)$

Answer 1

Answer: (A)

$(0,\frac{-5}{3})$

$\begin{array}{c}Wehavealine,\\ Co-ordinateofMis,\\ M_x=\frac{1\times -2+2\times 4}{3}=\frac{-2+8}{3}=\frac{6}{3}=2\\ \therefore M_x=2\\ M_y=\frac{1\times -3+2\times -1}{3}=\frac{-3-2}{3}=\frac{-5}{3}\\ \therefore M_y=\frac{-5}{3}\\ M=\left(2,\frac{-5}{3}\right)co-ordinatesofM\\ Co-ordinateofNis,\\ N_x=\frac{2\times -2+1\times 4}{3}=\frac{-4+4}{3}=0\\ \therefore N_x=0\\ N_y=\frac{2\times -3+1\times -1}{3}=\frac{-6-1}{3}=\frac{-5}{3}\\ \therefore N_y=\frac{-5}{3}\\ N=\left(0,\frac{-5}{3}\right)co-ordinatesofN.\\ So,correctoptionisA.\end{array}$