A) (7, 3)
B) (3, 7)
C) (35, 15)
D) (27, 21)
Correct Answer: A
Solution :
Let P (x, y) be the required point. Then, P divides AB internally in die ratio 3 : 2. |
Here, \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{3}{2}\] and \[\left( {{x}_{1}},\,{{y}_{1}} \right)=\left( 4,\,-3 \right)\]\[\left( {{x}_{2}},\,{{y}_{2}} \right)=\left( 9,\,7 \right)\] |
Then, \[P\left( x,\,y \right)=\] |
\[P\left( \frac{{{m}_{1}}{{x}_{2}}+{{m}_{2}}{{x}_{1}}}{{{m}_{1}}+{{m}_{2}}},\,\frac{{{m}_{1}}{{y}_{2}}+{{m}_{2}}{{y}_{1}}}{{{m}_{1}}+{{m}_{2}}} \right)\] |
[by section formula] |
\[=P\left( \frac{3\times 9+2\times 4}{3+2},\,\frac{3\times 7+2\times \left( -3 \right)}{3+2} \right)\] |
\[=P\left( \frac{27+8}{5},\frac{21-6}{5} \right)=P\left( \frac{35}{5},\,\frac{15}{5} \right)\] |
=P (7,3) |
Therefore, (7, 3) is the required point. |
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