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Question-205517




Question Number 205517 by BaliramKumar last updated on 23/Mar/24
Answered by mr W last updated on 23/Mar/24
AB=(√((5−4)^2 +(7−3)^2 ))=(√(17))  say D divides AB externally and  C divides AB internally.  DA=2AB  AC=(2/5)AB  DC=(2+(2/5))AB=((12(√(17)))/5) ✓  ⇒answer (a)
$${AB}=\sqrt{\left(\mathrm{5}−\mathrm{4}\right)^{\mathrm{2}} +\left(\mathrm{7}−\mathrm{3}\right)^{\mathrm{2}} }=\sqrt{\mathrm{17}} \\ $$$${say}\:{D}\:{divides}\:{AB}\:{externally}\:{and} \\ $$$${C}\:{divides}\:{AB}\:{internally}. \\ $$$${DA}=\mathrm{2}{AB} \\ $$$${AC}=\frac{\mathrm{2}}{\mathrm{5}}{AB} \\ $$$${DC}=\left(\mathrm{2}+\frac{\mathrm{2}}{\mathrm{5}}\right){AB}=\frac{\mathrm{12}\sqrt{\mathrm{17}}}{\mathrm{5}}\:\checkmark \\ $$$$\Rightarrow{answer}\:\left({a}\right) \\ $$
Commented by BaliramKumar last updated on 23/Mar/24
thanks  draw figure
$$\mathrm{thanks} \\ $$$$\mathrm{draw}\:\mathrm{figure} \\ $$
Commented by mr W last updated on 23/Mar/24
Commented by BaliramKumar last updated on 23/Mar/24
can i draw point D right side?
$$\mathrm{can}\:\mathrm{i}\:\mathrm{draw}\:\mathrm{point}\:\mathrm{D}\:\mathrm{right}\:\mathrm{side}? \\ $$
Commented by mr W last updated on 23/Mar/24
the same
$${the}\:{same} \\ $$
Commented by mr W last updated on 23/Mar/24
Commented by BaliramKumar last updated on 23/Mar/24
Commented by mr W last updated on 23/Mar/24
in this case C divides AB internally  in ratio 2:3. but D divides AB   externally in ratio 3:2. this is not   what the question states.
$${in}\:{this}\:{case}\:{C}\:{divides}\:{AB}\:{internally} \\ $$$${in}\:{ratio}\:\mathrm{2}:\mathrm{3}.\:{but}\:{D}\:{divides}\:{AB}\: \\ $$$${externally}\:{in}\:{ratio}\:\mathrm{3}:\mathrm{2}.\:{this}\:{is}\:{not}\: \\ $$$${what}\:{the}\:{question}\:{states}. \\ $$

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