Let \(P\) and \(Q\) be the points on the positive \(x\)-axis and positive \(y\)-axis respectively. A point \(N(2, 1)\) divides the line segment \(PQ\) in the ratio \(1 : 2\). What is the equation of the line?
\(x+y-3=0\)
Let \(P=(p,0)\) and \(Q=(0,q)\). Since \(N(2,1)\) divides \(PQ\) in the ratio \(1:2\), the section formula gives \(N=\left(\dfrac{2p}{3},\dfrac{q}{3}\right)\). Equating coordinates gives \(p=3\) and \(q=3\), so \(P=(3,0)\), \(Q=(0,3)\). The line through these points is \(x+y=3\), i.e. \(x+y-3=0\).
Similar Questions
What is the ratio in which the point \({\rm{C}}\left( { - \frac{2}{7},{\rm{\;}} - \frac{{20}}{7}} \right)\) divides the line joining the points A(-2, -2) and B(2, -4)?
The line x + y = 4 cuts the line joining P(-1, 1) and Q(5, 7) at R. What is PR ∶ RQ equal to ?
Important Questions from Sectional Formula
If the point C(1, 1) divides the line segment joining A(-2, 7) and B in the ratio 3 ∶ 2 internally, the coordinates of B are
What is the ratio in which the point \({\rm{C}}\left( { - \frac{2}{7},{\rm{\;}} - \frac{{20}}{7}} \right)\) divides the line joining the points A(-2, -2) and B(2, -4)?
In what ratio does the y-axis divide the line segment joining the points (-3, -4) and (1, 2)?
The line x + y = 4 cuts the line joining P(-1, 1) and Q(5, 7) at R. What is PR ∶ RQ equal to ?
Find the coordinates of the mid−point of the line segment joining the points A(−2, −5) and B(3, −1).
