distance from point to line

find the distance from the point (1,1) to the line y=3x+2 .

i did

y = 3x + 2
slope > 3
distance > -1/3
distance has slope -1/3 passes through the point (1,1)

y - y1 = m(x - x1) < point slope formula
y - 1 = (-1/3)(x-1)
y - 1 = -1/3x + 1/3
y = -1/3x + 1 1/3
y = -1/3x + 4/3

y=-1/3x + 4/3
y = 3x + 2
find the intersection point

-1/3x + 4/3 = 3x + 2
-x + 4 = 9x + 6
-10x = 2
x = -5

y = 3(-5)+2
y = -15+2
y = -13

the point (x,y) where the lines intersect is (-5,-13)

distance between (-5,-13) and (1,1)

d = sqrt[ (1 -(-5) )^2 + (1 - (-13) )^2 ]
d = sqrt[ (6)^2 + (14)^2 ]
d = sqrt[ 36 + 196 ]
d = sqrt[232]
d = 15.23154621
d = 15.2

CORRECT in my view

There's a formula for the distance between a point and line.

\(\displaystyle \L\\d=\left|\frac{Ax+By+C}{\sqrt{A^{2}+B^{2}}}\right|\)

Write your line equation in standard form.

\(\displaystyle y=3x+2\)...slope-intercept form

\(\displaystyle y-3x-2=0\)...standard form.

Pick a point on the line, say (0,2).
How far is it from (1,1)?

\(\displaystyle \sqrt{(1-0)^{2}+(1-2)^{2}}\;=\;\sqrt{2}\)

Whoops. I think this substantially refutes your result.

There is a formula for this sort of thing (as galactus has shown), but let's do it the hard way, as you attempted. You were so close!

-10*x = 2 <== You had it right up to this point. Try that division again.

tkhunny said:

Pick a point on the line, say (0,2).
How far is it from (1,1)?

\(\displaystyle \sqrt{(1-0)^{2}+(1-2)^{2}}\;=\;\sqrt{2}\)

Whoops. I think this substantially refutes your result.

There is a formula for this sort of thing (as galactus has shown), but let's do it the hard way, as you attempted. You were so close!

-10*x = 2 <== You had it right up to this point. Try that division again.

Click to expand...

hmmmm ok let me check

tkhunny said:

Pick a point on the line, say (0,2).
How far is it from (1,1)?

\(\displaystyle \sqrt{(1-0)^{2}+(1-2)^{2}}\;=\;\sqrt{2}\)

Whoops. I think this substantially refutes your result.

There is a formula for this sort of thing (as galactus has shown), but let's do it the hard way, as you attempted. You were so close!

-10*x = 2 <== You had it right up to this point. Try that division again.

Click to expand...

ok i get the same answer again and again
your saying -10x = 2 i am right on that
ohhhhhhhhhhh nooooooooooooooo i got it
i did -10/2
i had to do
2/-10
oh god thanks for telling me
now let me do it once again

now lets do it again
-10x = 2
x = -0.2

y = 3(-0.2)+2
y = -0.6 + 2
y = -1.4

the point (x,y) where the lines intersect is (-0.2,-1.4)

distance between (-0.2,-1.4) and (1,1)

d = sqrt[ ((1 - (-0.2))^2 + (1 - (-1.4))^2 ]
d = sqrt[ (1.2)^2 + (2.4)^2 ]
d = sqrt[ 1.44 + 5.76 ]
d = sqrt[ 7.2 ]
d = 2.683281573
d= 2.7

now it is correct
thanks

NEHA said:

y = -0.6 + 2
now it is correct

Click to expand...

Quit guessing. Be careful. You are closer still.

2 - 0.6 = +1.4

Why do you keep switching to decimals? Fractions are easier on this one, once you overcome your fear of fractions. It will be even easier with fractions when your batteries run out.

tkhunny said:

NEHA said:

y = -0.6 + 2
now it is correct

Click to expand...

Quit guessing. Be careful. You are closer still.

2 - 0.6 = +1.4

Why do you keep switching to decimals? Fractions are easier on this one, once you overcome your fear of fractions. It will be even easier with fractions when your batteries run out.

Click to expand...

ohhhhhhhhhh gosh my bad i put the negative sign

MANNNNNNNNNNN NEHA
ok now it has to be right lol
y = -0.6 + 2
y = 1.4

do the distance formula...i am not wirting that again
and get down to
d = sqrt[1.44 + 0.16]
d = sqrt1.6
d = 1.264911064
d = 1.3
pleaseeeeeeeeeeeee let this be right i believe it is

Is that \(\displaystyle \frac{4}{\sqrt{10}}\)? Then you're in business.

Did I encourage you to be more careful?

tkhunny said:

Is that \(\displaystyle \frac{4}{\sqrt{10}}\)? Then you're in business.

Did I encourage you to be more careful?

Click to expand...

i guess you did