Question

Find the distance from P to l.
Line l contains points (6,5) and (2,3).
Point P has coordinates (2,6).

Answer 1

vector from the line, and vector from a line point to the other point will be useful

Answer 2

(6,5) and (2,3). (2,6)
-2-3 -2-3 -2-3
--------------------
4,2 0,0 0,3
and the length of each vector
sqrt(20) 3

\[cos(a)=\frac{u.v}{|u|~|v|}\]
\[cos(a)=\frac{<4,2>\cdot <0,3>}{6 \sqrt5}\]
\[cos(a)=\frac{6}{6 \sqrt5}\]
\[a=cos^{-1}\left(\frac1{\sqrt5} \right) \]

Answer 3

sin of a times length of point vector should equal distance from line to point

Answer 4

another way would be to define the slope of the line, and perp it to get the line of the outer point; then see where the 2 lines cross and define the distance between those points

Answer 5

which method looks more familiar to you?