A) \[{{y}_{1}}:{{y}_{2}}\]
B) \[-{{y}_{1}}:{{y}_{2}}\]
C) \[{{x}_{1}}:{{x}_{2}}\]
D) \[-{{x}_{1}}:{{x}_{2}}\]
Correct Answer: B
Solution :
| [b] Let the X-axis divide the line segment joining \[P({{x}_{1}},{{y}_{1}})\]and \[Q({{x}_{2}},{{y}_{2}})\] in the ratio \[k:1\] at the P. |
| \[\therefore \] Coordinates of P are \[\left( \frac{k{{x}_{2}}+{{x}_{1}}}{x+1},\frac{k{{y}_{2}}+{{y}_{1}}}{k+1} \right)\] |
| Now, \[\frac{{{y}_{2}}k+{{y}_{1}}}{k+1}=0\] [P lies on X-axis] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,k=\frac{-{{y}_{1}}}{{{y}_{2}}}\]i.e., \[-{{y}_{1}}:{{y}_{2}}\] |
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