- #1
Helly123
- 581
- 20
Homework Statement
find the shortest distance from (0,0) to the line passing A(2,3) and B(3,5)
Homework Equations
## \frac{y-y1}{y2-y1} = \frac{x-x1}{x2-x1} ##
y-y1 = m (x-x1)
m1 * m2 = -1 (m1 perpendicular to m2)
The Attempt at a Solution
line passing A and B points
## \frac{y-3}{5-3} ## = ## \frac{x-2}{3-2} ##
y-3 = 2(x-2)
y = 2x - 1
m1 = 2
m2 = -1/2
the line perpendicular to line 1 and passing (0,0)
y -y1 = m(x-x1)
y-0=-1/2(x-0)
y' = -1/2x'
line 1 and line 2 intersect at (x,y)
y = y', x = x'
2x - 1 = -1/2x'
3/2x = 1
x = 2/3
y' = -1/2'x = -1/2(2/3) = -1/3
x,y = 2/3 , -1/3
distance is from (0,0) to (2/3 , -1/3)
distance = ## \sqrt{(2/3-0)^2 + (-1/3-0)^2} ##
distance = ## \sqrt{4/9 + 1/9} ##
distance = ## \sqrt{5}/3 ##
what's wrong? I got wrong answer