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=(y_2-y_1)/(x_2-x_1)`

`m=(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=(|ax_0+by_0+c|)/(√(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=(|2*6-1*-1+2|)/(√((2)^2+(-1)^2))`

`d=(15)/(√(5))`

`d=6.70820`...........Answer