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Angle of a line with the positive direct...

Angle of a line with the positive direction of the x-axis is `theta` . The line is rotated about some point on it in anticlockwise direction by angle `45^0` and its slope becomes `3.` Find the angle `theta`

Text Solution

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Originally,the slope of the line is `tan theta=m`.
Nowm, the slope of the line after rotation is 3.
Angle between the old position and the new position of lines is `45^@`. Therefore, we have
`tan45^@=(3-m)/(1+3m)`
or ` 1+3m=3-m`
or `4m=2`
or `m=(1)/(2)=tantheta`
or `theta=tan^(-1)(1/2)`
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Knowledge Check

  • The magnitude of the angle which the line y=-x makes with the positive direction of the x axis is -

    A
    `45^(@)`
    B
    `90^(@)`
    C
    `135^(@)`
    D
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  • The point (4,1) undergoes the following transformation successively (i) Reflection about the line y=x (ii) Translation through a distance 2 unit along the positive direction (x-axis) (iii)Rotation through on angle pi//4 about origin in anticlockwise direction. Then the co-ordinates of the final points

    A
    `(1/sqrt2,7/sqrt2)`
    B
    `(-1)/sqrt2,7/sqrt2)`
    C
    `(-1)/sqrt2,(-7)/sqrt2)`
    D
    none of these

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