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Question

The line passing through (7,3), (5,1) meets the x-axis at P. lf the line is rotated through an angle 30o in the anti-clockwise direction about P, then the slope of its new position is :

A
3
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B
13
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C
2+3
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D
23
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Solution

The correct option is D 23

Slop of line =3175=22=1θ=450

y1=x5y=x4

It meets x-axis at (4,0)

x=α+x1cosθy1sinθ

y=β+x1sinθ+y1cosθ

x=4+x1(32)y1(12)

y=0+x1(12)+y1(32)

y=x4

x12+y132=4+3x2y124

m=313+1×3131=3+1232=23


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