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Pooja singh Grade: 11

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?

7 years ago

Answers : (3)

vikas askiitian expert
510 Points

 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)


7 years ago
Pooja singh
18 Points

the answer given is incorrect

7 years ago
satyajit nandy
20 Points

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. 

7 years ago
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