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1. if a straight line through the point P(3,4) make an angle 30 degrees with x-axis and meets the line 12x + 5y +10=0 at Q, find the lenghth of PQ.
2. find X if (X,2) is an interior point of triangle ABC formed by
lines A+B=4,3A-7B=8,4A-B=31.
Hello Ashwin,
Its a nice question you have posted.
Answer to Q no 1.
Generic Equation of a straight line :
y- y1 = m(x -x1). For the question above , (x1,y1) = (3,4). And slope is given to be m =tan 30 = 1/sqrt(3).
So the equation of line becomes : y-4 = m(x-3) where m is as mentioned above.
Now the intersection point of two lines can be easily found out by just substituting value of y from one equation to another. Use value of sqrt(3) =1.732 and you the following intersection point:
Q= (-1.44,1.44)
From the two points P and Q
the distance PQ can be calculated as = 5.125
Hope this exaplanation solves your query. This question is just computational intensive.
Regards,
Ankit Jain
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