The distance between a point and a line is defined to be the shortest distance between the given point and any of the points on the given line. Answer the following questions, and then use what you have found to determine the distance between the point $\displaystyle {\left({5},{6}\right)}$ and the line $\displaystyle {y}={4}{x}+{2}$. Use exact values for all answers, i.e. no decimal approximations.

(a) The equation of the line perpendicular to $\displaystyle {y}={4}{x}+{2}$ and passing through $\displaystyle {\left({5},{6}\right)}$ is $\displaystyle {y}=$ Preview Question 6 Part 1 of 3   .

(b) The point where the line found in part (a) and $\displaystyle {y}={4}{x}+{2}$ intersect is Preview Question 6 Part 2 of 3   .

(c) The distance between $\displaystyle {\left({5},{6}\right)}$ and $\displaystyle {y}={4}{x}+{2}$ is Preview Question 6 Part 3 of 3   .