A) \[1:2\]internally
B) \[1:2\]externally
C) \[2:1\]internally
D) \[2:1\]externally
E) \[2:3\]externally
Correct Answer: D
Solution :
The midpoint of the line joining the points \[(-10,8)\]and\[(-6,12)\]is\[\left( \frac{-10-6}{2},\frac{8+12}{2} \right)\] ie,\[(-8,10)\]. Let\[(-8,10)\]divides the line joining the points\[(4,-2)\]and\[(-2,4)\]in the ratio\[m:n\]. \[\therefore \] \[\frac{m(-2)+n(4)}{m+n}=-8\] \[\Rightarrow \] \[-2m+4n=-8m-8n\] \[\Rightarrow \] \[6m=-12n\] \[\Rightarrow \] \[\frac{m}{n}=\frac{-2}{1}\] \[\therefore \]\[(-8,10)\]divides the line joining the points \[(4,-2)\]and\[(-2,4)\]in the ratio\[2:1\]externally.
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