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

calculus or geometry?

Answer 2

geometry

Answer 3

damn

Answer 4

ok we need the slope of the line, then the equation for the line perpendicular to the line through the point, and then where they intersect
i cannot think of another way to do it with geometry

Answer 5

slope of the line is easy enough, over 4 up 2 slope is \(\frac{1}{2}\) and so perpendicular line will have slope \(m=-2\)

Answer 6

equation for the line with slope \(m=-2\) through the point \((2,6)\) is
\[y-6=-2(x-2)\] or
\[y=-2x+10\]

Answer 7

equation of the line through the original points is \(y-3=\frac{1}{2}(x-2)\) or
\[y=\frac{1}{2}x+2\]

Answer 8

maybe @tanjung has a snappier way,
now i would find where the lines intersect
then compute the distance

Answer 9

ah, thank you very much, that all has helped me.

Answer 10

find the equation of l through points (6,5) and (2,3), that is
x-2y=-4 or x-2y+4=0
then, we calculate the distance P(2,6) to line's l, use formula :
d = |(ax1+by1+c)/sqrt(a^2+b^2)|
for a,b,c are the contant of line's l
and x1,y1 are coordinat's point of P

Answer 11

thank you very much(: