Question:
Find the distance of the point $(2,3)$ from the line $y=4$.
Solution:
Given: Point (2,3) and line y = 4
To find: The distance of the point (2, 3) from the line y = 4
Formula used: We know that the distance between a point $P(m, n)$ and a line $a x+b y+$ $c=0$ is given by,
$D=\frac{|a m+b n+c|}{\sqrt{a^{2}+b^{2}}}$
The equation of the line is $y-4=0$
Here $m=2$ and $n=3, a=0, b=1, c=-4$
$D=\frac{|1(3)-4|}{\sqrt{0^{2}+1^{2}}}$
$D=\frac{|3-4|}{\sqrt{0+1}}=\frac{|-1|}{\sqrt{1}}=1$
$D=1$
The distance of the point (2, 3) from the line y = 4 is 1 units