Q1 of 319 Page 24

A line passes through a point A (1, 2) and makes an angle of 600 with the x–axis and intercepts the line x + y = 6 at the point P. Find AP.

Given: (x1,y1) = A(1, 2), θ = 60°

To find:


Distance AP.


Explanation:


So, the equation of the line is


Formula Used:


⇒


⇒


Here, r represents the distance of any point on the line from point A (1, 2).


The coordinate of any point P on this line are


Clearly, P lies on the line x + y = 6


⇒ 1 + + 2 + = 6


⇒ = 3


⇒ r (√3 + 1) = 6


⇒ r =


Therefore, AP = 3(√3 – 1)


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