Q6 of 319 Page 24

Find the distance of the point (2, 3) from the line 2x – 3y + 9 = 0 measured along a line making an angle of 45° with the x–axis.

Given: (x1,y1) = A(2, 3), θ = 45°

To find:


Distance of point from line.


Explanation:


So, the equation of the line is


Formula Used:


⇒


⇒


⇒ x – y + 1 = 0


Let PQ = r


Then, the coordinate of Q are given by



⇒ x, y


The coordinate of point Q is


Clearly, Q lies on the line 2x – 3y + 9 = 0



⇒


⇒ r = 4√2


Hence, the distance of the point from the given line is 4√2.


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