1slope of d point joining origin to (3,4) is 4/3
slope of the required line is m=4/3 +11- 4/3= -7
|(3,4)|=5
Use (rcosθ,rsinθ) for the point
[339]
The new coordinates of point (3,4) when it is rotated through an angle of \Pi/4 about the origin in anticlockwise direction
Ans(-1/√2 , 7/√2)
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4 Answers
1
1Take
z=5e^{i\alpha}
where tan α = 4/3 and α is in the first quadrant
to rotate this by θ multiply by eiθ
then
z'=5e^{i(\alpha +\pi /4)}=5(cos(\alpha+\pi/4)+isin(\alpha+\pi/4)) \\=5(\frac{-1}{5\sqrt{2}}+i\frac{7}{5\sqrt{2}})\equiv (\frac{-1}{\sqrt{2}},\frac{7}{\sqrt{2}})
1This fetches the answer i guess ??
what kalyan did was also correct ....
1the pts lie on the circle...x2+y2=25 slope of the line joining the reqd pt=-1/7 difff the eqn of circle we get .m=.x1/y1=-1/7
now dividing the eqn of circle andthe puttin the value of x1/y1=-1/7 we get y1=7/√2 and x=-1/√2 ans
