A) 1 : 2
B) 7 : 2
C) 2 : 7
D) 4 : 1
Correct Answer: C
Solution :
| Let point \[P\left( -4,\,6 \right)\]divides the line segment joining the points A (- 6,10) and B (3, - 8) in the ratio \[{{m}_{1}}:\,\,{{m}_{2}}\]. |
|
| By using section formula, we get |
| \[\left( -4,\,6 \right)=\left( \frac{3{{m}_{1}}-6{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}},\frac{-8{{m}_{1}}+10{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)\] …. (i) |
| On equating .v-coordinate from both sides of Eq. (i), we get |
| \[-4=\frac{3{{m}_{1}}-6{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] |
| \[\Rightarrow \,\,-4\left( {{m}_{1}}+{{m}_{2}} \right)=3{{m}_{1}}-6{{m}_{2}}\] |
| \[\Rightarrow \,\,\,-4{{m}_{1}}-4{{m}_{2}}=3{{m}_{1}}-6{{m}_{2}}\] |
| \[\Rightarrow \,-4\,{{m}_{1}}-3{{m}_{1}}=-6{{m}_{2}}+4{{m}_{2}}\] |
| \[\Rightarrow \,\,\,\,\,-7\,{{m}_{1}}=-2{{m}_{2}}\] |
| \[\Rightarrow \,\,\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{2}{7}\] |
| \[{{m}_{1}}\,:\,{{m}_{2}}=2:7\] |
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