A) I quadrant
B) II quadrant
C) III quadrant
D) IV quadrant
Correct Answer: D
Solution :
| If P (x, y) divides the line segment joining \[A\left( {{x}_{1}},\,{{y}_{1}} \right)\]and \[B\left( {{x}_{2}},\,{{y}_{2}} \right)\]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 \[n=2\] |
| \[\therefore \,\,\,x=\frac{1\left( 3 \right)+2\left( 7 \right)}{1+2},\,y=\frac{1\left( 4 \right)+2\left( -6 \right)}{1+2}\] |
| [by section formula] |
| \[\Rightarrow \,\,\,x=\frac{3+14}{3},\,y=\frac{4-12}{3}\] |
| \[\Rightarrow \,\,x=\frac{17}{3},\,y=-\frac{8}{3}\] |
| So, \[\left( x,\,y \right)=\left( \frac{17}{3},\,-\frac{8}{3} \right)\]lies in IV quadrant. [since, in IV quadrant, x-coordinate is positive and y-coordinate is negative] |
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