A) I quadrant
B) II quadrant
C) III quadrant
D) IV quadrant
Correct Answer: D
Solution :
| [d] If \[P(x,y)\] divides the line segment joining \[A({{x}_{1}},{{y}_{1}})\]and \[B({{x}_{2}},{{y}_{2}})\] internally in the ratio \[m & :n,\] then |
| \[x=\frac{m{{x}_{2}}+n{{x}_{1}}}{m+n}\]and \[y=\frac{m{{y}_{2}}+n{{y}_{1}}}{m+n}\] |
| Given that \[{{x}_{1}}=7,\]\[{{y}_{1}}=-6,\]\[{{x}_{2}}=3,\]\[{{y}_{2}}=4,\]\[m=1\]and \[n=2\] |
| \[\therefore \,\,x=\frac{1(3)+2(7)}{1+2},\,\,\,y=\frac{1(4)+2(-6)}{1+2}\] |
| [By section formula] |
| \[\Rightarrow \,\,\,\,x=\frac{3+14}{3},\,y=\frac{4-12}{3}\,\,\,\,\,\,\,\,\Rightarrow \,\,x=\,\frac{17}{3},\,\,y=-\frac{8}{3}\] So, \[(x,y)=\left( \frac{17}{3},-\frac{8}{3} \right)\] lies in IV quadrant. |
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