Question

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 points of intersection

Answer 1

SoluTion :-

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

$\therefore \fbox { Coordinates of P are}$

$\tt {\frac{(6k - 2)}{(k+1)} , \frac{(3k-5)}{(k+1)}}$

P lies on x – 3y = 0

$\implies \frac{(6k - 2)}{(k + 1)} = \frac{3(3k - 5)}{(k + 1)}$

6k - 2 = 9k - 15

$\tt {k = \frac {13}{3}}$

$\therefore \fbox { Ratio is 13 : 3}$

$\sf {\implies Coordinates\ of\ P\ are (\frac{9}{2}, \frac{3}{2} )}$

$\rule {130}{2} \ Be\ Brainly \ \star$