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The line joining two points P(1,0),Q(2,1) is rotated about P in clockwise direction through an angle of 15degrees. Find the coordinates of the new position?
Q1 be the new point after rotation....length of the segment PQ1 will remain same after rotation....
slope of PQ = 2-1/1-0=1 =tan-1pi/4 .............1
@ = pi/4 (@ is inclination with x AXIS)
after rotation let it makes an angle @1 with X axis then
@1 = pi/4+pi/12 (15degree = pi/12)
@1 = pi/3 .............2
we have
X2-X1/cos@ = Y2-Y1/sin@ = d (d is distance bw two points)
X2-1/cospi/3 = Y2-0/sinpi/3 = 1
X2 = 3/2 , Y2 =31/2/2
Q1 = (3/2,sqrt3/3)
the answer given is incorrect
As the line rotates through 15 degree, the slope of the new line will be 30 degrees.But the length of both the lines will remain same.
let (x1,y1) be the new position of point Q.
now { y1/x1-1}= 1/sq. root of 3
=y1=(x1-1)/sq. root of 3.
again sq. root of {(x1-1)^+ y1^2}= sq. root of 2
which gives x1= sq. root of (3/2)+1 and y1=1/sq. root of 2.
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