Question

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

Answer 1

Answer:

The distance between line 6 x - y = - 3 and point (6,2) is$\sqrt{37}$

Step-by-step 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 = $\frac{\begin{vmatrix}6\times 6 & + (-1)\times 2 & + 2\end{vmatrix}}{\sqrt{6^{2}+(-1)^{2}}}$

or, d = $\frac{36-2+3}{\sqrt{37} }$

∴   d = $\frac{37}{\sqrt{37} }$

I.e d = $\sqrt{37}$

Hence The distance between line 6 x - y = - 3 and point (6,2) is$\sqrt{37}$   Answer