Question

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

Answer 1

Answer:

$\sqrt{37}$ units

Step-by-step explanation:

If we draw a perpendicular from point (6,2) on the line 6x - y = - 3, then we have to find the length of the perpendicular.  

We know the formula of length of perpendicular from a point $(x_{1}, y_{1} )$ to the straight line ax + by + c = 0 is given by  

$\frac{|ax_{1} + by_{1} +c |}{\sqrt{a^{2}+b^{2}}}$

Therefore, in our case the perpendicular distance is  

$\frac{|6(6)-2+3|}{\sqrt{6^{2} +(-1)^{2} } } = \frac{37}{\sqrt{37} } = \sqrt{37}$  units. (Answer)