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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.
Solution
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
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