Question

grh

Answer 1

@sourwing

Answer 2

use the distance formula , you want the distance between (0,0) and (x,y) , where (x,y) is on the line y = mx + b

Answer 3

so the distance between points (0,0) and ( x, mx + b ) , by substitution

Answer 4

d = sqrt ( (x - 0) ^2 + ( mx + b - 0) ^2 )
d = sqrt[ x^2 + (mx+b)^2 ]

Answer 5

now take the derivative, since you want to minimize this

Answer 6

im in precalc im not supposed to be using derivatives even if i do know them

Answer 7

so solve a complicated geometry argument, good luck

Answer 8

wow thats harsh

Answer 9

seriously?

Answer 10

hahaha

Answer 11

im in precalculus? wtf i sprecalculaus

Answer 12

math is math

Answer 13

yeah i know but teacher said that he didnt want us using advanced stuff even if we knew it so i can't

Answer 14

ok, the shortest distance from y = mx + b , to (0,0) will be on a perpindicular line

Answer 15

so draw y = mx + b , a generic line , and the closest to (0,0) will be a segment that is perpindicular, i cant draw it here unfortunately

Answer 16

thats what i di the first time and i kept getting the origin as my point

Answer 17

draw y = mx + b so that it does not go through teh origin

Answer 18

yeah i used 2x+2

Answer 19

we need this to be general .
y = mx + b , the slope of the perpindicular line to it is -1/m.
now this perpindicular goes through (0,0). so you want a line that has slope -1/m and goes through (0,0).
so the perpindicular is y = -1/m * x

Answer 20

, now we find where y = -1/m*x and y = mx + b intersect ,

Answer 21

-1/m * x = mx + b , solve for x

Answer 22

x=b/((-1/m)-m)

Answer 23

how did you get that?

Answer 24

x((-1/m)-m)=b
x=b/((-1/m)-m)

Answer 25

oh nevermind i see :)

Answer 26

, ok simplifying we get
x = -mb / ( m^2 + 1 )

Answer 27

how did you get that?

Answer 28

so thats your x coordinate

Answer 29

how did you go from x=b/((-1/m)-m) to x = -mb / ( m^2 + 1 )

Answer 30

first simplify the denominator
-1/m - m = -1/m - m/1 = -1/m - m^2/m = (-1 - m^2) / m

Answer 31

never mind i got it know

Answer 32

now*

Answer 33

ok so thats your x coordinate, to find the y coordinate plug that into y = mx + b , for x

Answer 34

heh, it turns out the calculus way is harder,

Answer 35

haha cool

Answer 36

actually i take that back, its easier :)

Answer 37

at least to find the x coordinate

Answer 38

without calculus i had to invoke some geometry principles ;)

Answer 39

err, regarding the slope thingy

Answer 40

its funny that we both asked . how did you get that,

Answer 41

now do you have any trouble with finding the y coordinate