Question

Find the exact distance between the line 6x-y=3 and the point (6,2). Show your work. Explain your answer.

Answer 1

Using the distance formula, you can solve to show that the distance between 6x-y= 3 = 37/ sqrt 37, or sqrt 37

Explanation:

Answer 2

The distance of point ( 6 , 2 ) from line 6 x - y = 3 is
`(31)/(√(37) )` unit .

Explanation:

Given as :

The equation of line is 6 x - y = 3

And The points is ( 6 , 2 )

Let The distance between the line and points is d unit

So, The distance of point from the line =
`\frac{\begin{vmatrix}ax & +b y & + c\end{vmatrix}}{\sqrt{a^(2)+b^(2)}}`

Or, d =
`\frac{\begin{vmatrix}6* x & +(-1)*  y & + (-3)\end{vmatrix}}{\sqrt{6^(2)+(-1)^(2)}}`

Or, d =
`\frac{\begin{vmatrix}6* 6 & +(-1)*  2 & + (-3)\end{vmatrix}}{\sqrt{6^(2)+(-1)^(2)}}`

Or, d =
`(36 - 2 - 3)/(√(37) )`

∴ d =
`(31)/(√(37) )` unit

Hence The distance of point ( 6 , 2 ) from line 6 x - y = 3 is
`(31)/(√(37) )` unit . Answer