Q.Find the distance of the line x − y − 4 = 0 from the point P(4,1) measured along the line making an angle of 135° with the positive X-axis.

For line $x-y-4=0$ ($a=1,b=-1,c=-4$), point $P(4,1)$, and direction $\theta=135°$ ($\cos135°=-\dfrac{\sqrt2}{2}$, $\sin135°=\dfrac{\sqrt2}{2}$): the value of the line's expression at $P$ is $4-1-4=-1$. The directional-distance denominator is $a\cos\theta+b\sin\theta=1\left(-\dfrac{\sqrt2}{2}\right)+(-1)\left(\dfrac{\sqrt2}{2}\right)=-\sqrt2$. So $ …

Apply the directional-distance formula measured along a line at a fixed angle, evaluat …

• Using the plain perpendicular-distance formula instead of the direction-dependent one, since the question specifically asks for distance measured …