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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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