Question

The line joining P (-5, 6) and Q (3, 2) intersects the y-axis at R. PM and QN are perpendiculars from P and Q on the x-axis. Find the ratio PR: RQ. 

Answer 1

R(O, y) is the point on the y-axis that divides PQ.

Let the ratio in which PQ is divided by R be m:n.

Now, R(o,y),(x1,y1)=(-5,6) and (x2,y2)=(3,2) and the ratio is m:n. 

`0 = ("m x"_2 + "nx"_1)/("m + n")`

`=> 0 = (3"m" - 5"n")/("m + n")`

⇒ 0 = 3m = 5n

⇒ 3m = 5n

`=> "m"/"n" = 5/3`

⇒ m : n = 5 : 3

⇒ PR : RQ = 5 : 3