Geometry (C10)

Find the ratio in which the line x – 3y = 0 divides the line segment joining the points (–2, –5) and (6, 3). Find the coordinates of the point of intersection.

Answer

Let the line x – 3y = 0 intersect the segment joining A(–2, –5) and B(6, 3) in the ratio k : 1.

∴ Coordinates of P are

(6k–2)/(k+1), (3k–5)/(k+1)

P lies on x – 3y = 0

⇒ (6k – 2)/(k + 1) = 3(3k – 5)/(k + 1)

6k - 2 = 9k - 15

k = 13/3

∴ Ratio is 13 : 3

⇒ Coordinates of P are (9/2, 3/2)