Question

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

Answer 1

`√(37)` units

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

`\fracax_(1) + by_(1) +c {\sqrt{a^(2)+b^(2)}}`

Therefore, in our case the perpendicular distance is

`\frac{\sqrt{6^(2) +(-1)^(2) } } = (37)/(√(37) ) = √(37)` units. (Answer)