If θ is the angle which the straight line joining the points (x 1 , y 1 ) and (x 2 , y 2 ) subtends at the origin, prove that and .

Question

Philoid · Accepted Answer

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 = y_1x1

Slope of OB = m₂ = y_2x2

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

∴

⇒

Now,

As we know that

∴

⇒

Hence proved.