A) \[\left( \frac{13}{3},\frac{56}{3} \right)\]
B) \[\left( \frac{56}{3},\frac{13}{3} \right)\]
C) \[\left( \frac{13}{4},\frac{56}{3} \right)\]
D) \[\left( \frac{56}{3},\frac{13}{4} \right)\]
Correct Answer: A
Solution :
| Given points: \[(3,20)\] and \[(7,16)\] |
| Here, \[{{x}_{1}}=3,\]\[{{y}_{1}}=20,\]\[{{x}_{2}}=7,\]\[{{y}_{2}}=16\]and ratio \[{{m}_{1}}:{{m}_{2}}=1:2\] |
| Let the point of division be \[p(x,y):\] |
| Then from division formula: |
| \[x=\frac{{{m}_{1}}{{x}_{2}}+{{m}_{2}}{{x}_{1}}}{{{m}_{1}}+{{m}_{2}}}\]and \[y=\frac{{{m}_{1}}{{y}_{2}}+{{m}_{2}}{{y}_{1}}}{{{m}_{1}}+{{m}_{2}}}\] |
| \[=\frac{1\times 7+2\times 3}{1+2}=\frac{13}{3}=\frac{1\times 16+2\times 20}{1+2}=\frac{56}{3}\] |
| Therefore, the coordinate of the green flag is \[\left( \frac{13}{3},\frac{56}{3} \right)\] |
| So, option [a] is correct. |
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