
#1
Mar1311, 10:06 AM

P: 9

Hi,
I've reached a question in a maths text book I'm reading that I'm having some trouble with. Any help/suggestion would be greatly appreciated. The question it self is short but there are a couple of paragraphs which set it up that I've copied directly out of the book. 1. The problem statement, all variables and given/known data We distinguish a positive and a negative side of a directed line l as follows. Let P be any point not on l, and let Q be the foot of the perpendicular to l through P. Then P is on the positive or negative side of l according as the angle from l to the directed line QP is 90 or 90 degrees. We shall now determine the equation of a directed line l. We draw through the orign O a line m perpendicular to l, and direct m so that the angle from it to l is 90 degrees. The angle from the directed xaxis to m will be called [tex]\beta[/tex]. Then [tex]\alpha = 90^{\circ} + \beta , \sin \alpha = \cos \beta , cos\alpha = \sin \beta[/tex]. Let R with coordinates x_{1}, y_{1} be the point where m meets l. We shall denote by d the directed distance OR on directed m. Show that d is positive if and only if O lies on the negative side of l. 2. Relevant equations 3. The attempt at a solution The question states that d should be positive if and only if O is on the negative side of l. However I've attached a simple sketch where (i think) d is positive when O is on the positive side (the black line being l and the green one being d and m). I'm not sure what I've done wrong to get this result, any pointers would be great :) thanks alot babak 


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