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Grade 11Analytical Geometry

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.

Profile image of ashwin gopalan
16 Years agoGrade 11
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4 Answers

Profile image of Askiitians Expert Ankit Jain- IIT Bombay
15 Years ago

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

Profile image of Angad Sethi
10 Years ago
Actually what you can do is make use of the parametric form which is
x-x'/cos theta=y-y'/sin theta=r
Here theta=π/6
x'=3
y'=4
Apply the values and find the values of x and y
x=6+r√3/2
y=r+8/2
Using equation 12x+5y+10=0
r=132/12√3+5
Thus this is the distance.
Profile image of Vikas TU
10 Years ago
In second part plot the three eqn.s on x -y axis and discover by satifying the origin in those three eqns.
u will get as:
 
3A -7B >=8
A + B >= 4
4A – B
 
satify the point (X,2) in all these three eqns.
we get,

X>= 22/3 …............(1)
X>=2/3. …...........(2)
X
TAKING the intersection of (1) (2) and (3)
we get,
X belongs to [22/3, 33/4]
Profile image of Kj
8 Years ago
This question can easily be solved by using parametric eqn firstly find value of x and y in the form of r then put the values in the given eq

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