Question

Find the distance between the line y = -3x + 8 and the point (-1, 1)

Answer 1

Answer: The required distance = $\sqrt{10}$ units

Step-by-step explanation:

The shortest distance from a point $(x_1,y_2)$ to a line $(Ax+By+C=0)$ is the perpendicular distance.

$d=\dfrac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2\\}}$

Given: Equation of line :  = y= -3x + 8 i.e. 3x+y-8=0

Point = (-1,1)

Distance between them = $\dfrac{|3(-1)+1(1)-8}{\sqrt{(3)^2+(1)^2|}}$

$=\dfrac{|-3+1-8|}{\sqrt{9+1}}\\\\=\dfrac{10}{\sqrt{10}}\\\\=\sqrt{10}$

Hence, the required distance = $\sqrt{10}$ units