A line \((\sin\theta)x + (\cos\theta)y = \sin 2\theta\) cuts the coordinate axes at points \(P\) and \(Q\). Let \(M\) be the midpoint of the line segment \(PQ\). What is the distance of \(M\) from the origin?
\(1\)
Putting \(y=0\) gives the \(x\)-intercept \(P=(2\cos\theta,0)\), and putting \(x=0\) gives the \(y\)-intercept \(Q=(0,2\sin\theta)\), using \(\sin2\theta=2\sin\theta\cos\theta\). The midpoint is \(M=(\cos\theta,\sin\theta)\), so its distance from the origin is \(\sqrt{\cos^2\theta+\sin^2\theta}=1\).
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Important Questions from General Equation of a Line
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If (2, 1), (–1, –2), (3, 3) are the midpoints of the sides BC, CA, AB of a triangle ABC, then equation of the line BC is
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