- #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