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Question Number 25712 by ajfour last updated on 13/Dec/17

Commented by ajfour last updated on 13/Dec/17

solution to Q.25706

$${solution}\:{to}\:{Q}.\mathrm{25706} \\ $$

Answered by ajfour last updated on 13/Dec/17

slope of L_1 =slope of OB =(1/3)  eqn. of L_1 :  y−3=(1/3)(x+1)  slope of AB =((1−3)/(3−(−1))) =−(1/2)  slope of L_2 =−(1/(slope of AB)) =2  eqn. of L_2 :  y−1=2(x−3)  As C lies on L_1  and L_2 ,  y_c =3+(1/3)(x_c +1)=1+2(x_c −3)  ⇒  x_c (2−(1/3))=8+(1/3)  or  x_c = 5  and y_c =1+2(5−3)=5  Hence C(5,5) .

$${slope}\:{of}\:{L}_{\mathrm{1}} ={slope}\:{of}\:{OB}\:=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${eqn}.\:{of}\:{L}_{\mathrm{1}} :\:\:{y}−\mathrm{3}=\frac{\mathrm{1}}{\mathrm{3}}\left({x}+\mathrm{1}\right) \\ $$$${slope}\:{of}\:{AB}\:=\frac{\mathrm{1}−\mathrm{3}}{\mathrm{3}−\left(−\mathrm{1}\right)}\:=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${slope}\:{of}\:{L}_{\mathrm{2}} =−\frac{\mathrm{1}}{{slope}\:{of}\:{AB}}\:=\mathrm{2} \\ $$$${eqn}.\:{of}\:{L}_{\mathrm{2}} :\:\:{y}−\mathrm{1}=\mathrm{2}\left({x}−\mathrm{3}\right) \\ $$$${As}\:{C}\:{lies}\:{on}\:{L}_{\mathrm{1}} \:{and}\:{L}_{\mathrm{2}} , \\ $$$${y}_{{c}} =\mathrm{3}+\frac{\mathrm{1}}{\mathrm{3}}\left({x}_{{c}} +\mathrm{1}\right)=\mathrm{1}+\mathrm{2}\left({x}_{{c}} −\mathrm{3}\right) \\ $$$$\Rightarrow\:\:{x}_{{c}} \left(\mathrm{2}−\frac{\mathrm{1}}{\mathrm{3}}\right)=\mathrm{8}+\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${or}\:\:{x}_{{c}} =\:\mathrm{5}\:\:{and}\:{y}_{{c}} =\mathrm{1}+\mathrm{2}\left(\mathrm{5}−\mathrm{3}\right)=\mathrm{5} \\ $$$${Hence}\:{C}\left(\mathrm{5},\mathrm{5}\right)\:. \\ $$

Commented by tawa tawa last updated on 13/Dec/17

Wow. God bless you sir.

$$\mathrm{Wow}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

Commented by tawa tawa last updated on 13/Dec/17

God bless you sir. Now i understand.

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{Now}\:\mathrm{i}\:\mathrm{understand}. \\ $$

Commented by tawa tawa last updated on 13/Dec/17

Sir. why is slope of L_1  = slope of OB ?. please

$$\mathrm{Sir}.\:\mathrm{why}\:\mathrm{is}\:\mathrm{slope}\:\mathrm{of}\:\mathrm{L}_{\mathrm{1}} \:=\:\mathrm{slope}\:\mathrm{of}\:\mathrm{OB}\:?.\:\mathrm{please} \\ $$

Commented by ajfour last updated on 13/Dec/17

given in question: L_1  parallel to  OB. parallel lines have same  slopes.

$${given}\:{in}\:{question}:\:{L}_{\mathrm{1}} \:{parallel}\:{to} \\ $$$${OB}.\:{parallel}\:{lines}\:{have}\:{same} \\ $$$${slopes}. \\ $$

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