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let the coordinates of the two points A and B be (1,2) and (7,5) respectively. the line AB is rotated through 45 degrees in anti clockwise direction about the point of trisection of AB which is nearer to B. th equation of the lline in new position.



10-Oct-2015 12:47 PM
~12

Answers (1)


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Take difference between points:

x2 - x1 = 6
Since you want the point of trisection nearer to 'B', take 2/3 rd of the difference. 2/3rd of difference = 6*(2/3) = 4

Similarly for difference in y: y2 - y1 = 3
2/3rd of (y2-y1) = 3*(2/3) = 2

Now the trisecting point near 'B' will be: [ Starting point + adjusted difference ]

= (1,2) + (4,2) = (5,4)

Therefore, (5,4) is the point about which the line is rotated, and thus our final line will also pass through (5,4).

Original slope of line(m) = y2-y1/(x2-x1) = 1/2. Thus angle made by original line = tan-1(1/2).

Rotated by 45 deg in anti-clockwise, New angle made with x-axis = 45 + tan-1(1/2)

Therefore, slope of new line = tan(45 + tan-1(1/2) )

Using property: tan(A+B) = (tanA + tanB) / (1 - tanAtanB) and the property tan(tan-1x) = x, we will get the slope equal to 3.

Now we have the slope(m) = 3 and the point (5,4) of the resultant line, thus calculating the line equation as:

y-y1=m(x-x1)

y - 4 = 3(x - 5)

y = 3x -11

 

 



10-10-2015 13:30
~48

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