Q5 of 319 Page 24

If θ is the angle which the straight line joining the points (x1, y1) and (x2, y2) subtends at the origin, prove that and .

To prove:


and


Assuming:


A (x1, y1) and B (x2, y2) be the given points and O be the origin.


Explanation:



Slope of OA = m1 = y1x1


Slope of OB = m2 = y2x2


It is given that θ is the angle between lines OA and OB.


∴



⇒


Now,


As we know that


∴


⇒


⇒


Hence proved.


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