Question

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

Answer 1

Attached

Explanation:

Answer 2

The distance between line 6 x - y = - 3 and point (6,2) is
`√(37)`

Explanation:

Given equation of line as :

6 x - y = - 3

And The points be ( 6 , 2 )

Let The distance between line and points = d

So , from point to line distance formula

d =
`\frac{\begin{vmatrix}ax & + by & + c\end{vmatrix}}{\sqrt{a^(2)+b^(2)}}`

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

∵ points is ( 6 , 2 )

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

or, d =
`(36-2+3)/(√(37) )`

∴ d =
`(37)/(√(37) )`

I.e d =
`√(37)`

Hence The distance between line 6 x - y = - 3 and point (6,2) is
`√(37)` Answer