A) \[\left( \frac{3}{2},-\frac{5}{2} \right)\,,\left( -\frac{3}{2},-\frac{13}{4} \right)\]
B) \[\left( -\frac{3}{2},\frac{5}{2} \right)\,,\left( \frac{3}{2},\frac{13}{4} \right)\]
C) \[\left( 1,-\frac{8}{3} \right)\,,\left( -1,-\frac{10}{3} \right)\]
D) None of these
Correct Answer: C
Solution :
Let\[A(3,\,-2)\],\[B\,(-3,\,\,-4)\] and two points C and D are the trisection points of AB. Obviously C divides the line AB in 1 : 2, therefore coordinates of C are \[\left( \frac{1(-3)+2(3)}{1+2},\,\frac{1(-4)+2(-2)}{1+2} \right)=\left( 1,\,\,-\frac{8}{3} \right)\]. Similarly D divides the line AB in 2 : 1, hence coordinates of D are \[\left( \frac{2(-3)+1(3)}{2+1},\,\frac{2(-4)+1(-2)}{2+1} \right)=\left( -1,\,\,-\frac{10}{3} \right)\].
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