Question

determine the shortest distance from the point (6,3) to the line y=-2x+1

Answer 1

the shortest distance is the perpendicular distance which is 14/sqrt(5)

Answer 2

two ways, calc way and thinking way

Answer 3

basically we shld find the right bisector rite?

Answer 4

thinking way is to realize that the line connecting the point and the other line giving the shortest distance will be perpendicular to it and therefore have slope of \[\frac{1}{2}\]

Answer 5

so you have a line with slope \[\frac{1}{2}\] through (6,3). find the equation of the line and then see where they intersect by setting the two lines equal

Answer 6

the equation is
\[y-3=\frac{1}{2}(x-6)\]
\[y-3=\frac{1}{2}x-3\]
\[y=\frac{1}{2}x\]

Answer 7

now solve
\[-2x+1=\frac{1}{2}x\]

Answer 8

\[x=\frac{2}{5}\]

Answer 9

so \[y=\frac{1}{5}\]

Answer 10

then use distance formula.

Answer 11

thank u