Question

the distance is approximately

Answer 1

We are given two points of a line

(-2, -2) and (1,4)

Equation of line:

Firstly , we will find slope

(-2, -2) and (1,4)

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{4+2}{1+2}$

$m=2$

now, we can find equation of line

$y-y_1=m(x-x_1)$

now, we can plug values

and we get

$y+2=2(x+2)$

$2x-y+2=0$

Distance:

now, we can use distance formula

$d=\frac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}}$

firstly , we will find a and b

a=2 and b=-1

point is (6,-1)

so, xo=6 and yo=-1

we can plug values

and we get

$d=\frac{|2*6-1*-1+2|}{\sqrt{(2)^2+(-1)^2}}$

$d=\frac{15}{\sqrt{5}}$

$d=6.70820$...........Answer