Question

Find the distance of the point $\left(4,2\right)$ from the line passing through the points $\left(4,1\right)$ and $\left(2,3\right)$

Answer 1

Let the points $A(4,1)$ and $B(2,3)$.

We know that the equation of line passing through two points,

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-1=\frac{3-1}{2-4}(x-4)$

$y-1=\frac{2}{-2}(x-4)$

$y-1=-1(x-4)$

$y-1=-x+4$

$x+y-5=0$ ……. (1)

Since, the distance from the point $(4,2)$ to above line

$d=\frac{1\times 4+1\times 2-5}{\sqrt{1^2+1^2}}$

$d=\frac{4+2-5}{\sqrt{2}}$

$d=\frac{1}{\sqrt{2}}$

Hence, this is the answer.