sketch the triangle with vertics A(-5,12), B(4,-2) and C(1,-6)
Find the slope of the side AC.
Find the slope of the altitude form point B to side AC
fIND an equation for the line that includes the altitude from point B to side AC

- toxicsugar22

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- anonymous

Do you recall the formula for the slope of a line given 2 points on the line?

- toxicsugar22

yes

- anonymous

So use it to find the slope of the side AC.

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## More answers

- anonymous

Once you have that you can find the perpendicular slope by taking the negative reciprocal

- anonymous

which is the slope of the altitude from B to the side AC. Then with that slope you can write the equation of the line with that slope that intersects B.

- toxicsugar22

im guessing -3

- toxicsugar22

is that right

- anonymous

-3 is the slope of AC

- toxicsugar22

ok

- anonymous

So what is the slope perpendicular to that?

- toxicsugar22

so what would be the equatin

- toxicsugar22

1/-3

- toxicsugar22

right

- anonymous

No, negative reciprocal is perpendicular.

- anonymous

so 1/3

- anonymous

So now, you have a point B and the slope. Do you know the formula for the equation of the line given a point and a slope?

- toxicsugar22

y=1/3x+2

- toxicsugar22

is that right

- toxicsugar22

is thais right

- anonymous

I don't think so. It should be \(y+2 = \frac{1}{3}(x-4)\)

- toxicsugar22

i think we put it in slope intecept form

- anonymous

sure, but I don't think if you do you'll get the answer you had before

- toxicsugar22

ok

- toxicsugar22

vut can u help me get me put that in slope inetcept form

- anonymous

Well start by distributing the 1/3, then subtract 2 from both sides

- toxicsugar22

y+2=1/3(x-4)
can u help me put tis in slpo intecept orm

- toxicsugar22

can u help me

- anonymous

did you distribute the 1/3?

- toxicsugar22

how do u do -4/3-2

- anonymous

convert -2 into an improper fraction (with a 3 in the denominator)

- toxicsugar22

i got y+2=1/3x-4/3

- toxicsugar22

is that right then i subract 2 from both sides

- anonymous

yes

- toxicsugar22

then i get y=1/3x-3.3

- toxicsugar22

is this write

- anonymous

-3.33333 = -10/3

- toxicsugar22

thanks you so much

- toxicsugar22

The center of a circle is the point C(2,4), and P(-1,6) is a point on the circle. Find the equation of the line tangent to the circle at the point P.

- toxicsugar22

can u help with this

- anonymous

umm.. it's pretty nearly the same problem, just with different numbers

- toxicsugar22

ok

- toxicsugar22

but can u help me

- anonymous

draw the picture of what they're describing, and recall what we did in this last problem and see if you can figure out how the problems are similar.

- toxicsugar22

i tried please can u help me

- anonymous

what did you try?

- toxicsugar22

i tried doing it but idid not get it

- toxicsugar22

doing the pomble

- toxicsugar22

can u help me

- anonymous

what did you _do_ when you tried?

- toxicsugar22

idid (2,4) and (- 1and 6) and added the x and y

- toxicsugar22

please can u help, I will be greatful to you

- anonymous

what were you trying to find when you did that?

- toxicsugar22

idk i thought that was how u do that

- anonymous

do what?

- toxicsugar22

the question

- anonymous

Are you trying to find something?

- toxicsugar22

yes the equation

- anonymous

the equation of what?

- toxicsugar22

The center of a circle is the point C(2,4), and P(-1,6) is a point on the circle. Find the equation of the line tangent to the circle at the point P

- anonymous

I know what the problem says, I'm asking you what you think. You do think right? ;)

- toxicsugar22

i am finding it difficult please can u help me

- anonymous

What are you trying to find here?

- toxicsugar22

the equation i guess

- anonymous

The equation of what?

- toxicsugar22

the slope

- toxicsugar22

the slope

- anonymous

"Find the equation of the line tangent to the circle at the point P"

- anonymous

What does that sentence mean?

- toxicsugar22

i think it means that the line is touching line p

- toxicsugar22

is that right

- toxicsugar22

is this righ t

- anonymous

The line is touching the point P that's on the circle, but what else do you know about it?

- toxicsugar22

idk

- anonymous

well, specifically how does it relate to the radius of the circle through the point P?

- toxicsugar22

is the slope -3/2

- toxicsugar22

is it right

- anonymous

that is the slope of the radius (line between the center and P). The trick is to realize that the slope of the tangent will be perpendicular to the radius.

- toxicsugar22

so it will be 2/3

- toxicsugar22

is that right

- anonymous

that is the slope. now use the point p to find the equation like we did before

- toxicsugar22

so we do (-1,-6)

- toxicsugar22

so it would be y+6=2/3(x+1)

- toxicsugar22

is that right

- anonymous

I thought P was (-1,6), so it would be y-6 = 2/3(x+1)

- toxicsugar22

oh yeah sorry your right

- toxicsugar22

if i put it in slope intecept orm it would be y=2/3x+6.67

- toxicsugar22

is this right

- anonymous

yeah

- toxicsugar22

but is the 6.67 right or can i put it in a fraction

- anonymous

you can make it a fraction

- toxicsugar22

how can u show me

- anonymous

How many 3rds are there in 6 wholes?

- toxicsugar22

so id it 20/3

- toxicsugar22

wait i think we messed up it would be y+6=2/3(X-1)

- toxicsugar22

i think that is right

- toxicsugar22

i think that is right

- anonymous

If the point P is (-1,6) then the equation would be y-6=2/3(x+1)
The formula for point-slope is:
\[y-y_1 = m(x-x_1)\]
Where \(x_1,y_1\) are the x,y values of your point

- toxicsugar22

so would it be y=2/3x+3/20

- anonymous

no

- anonymous

I can tell because the 3/20 is less than 1, but we added 6 to both sides, so it should be bigger than 1

- toxicsugar22

y=2/3x+20/3

- anonymous

yes

- toxicsugar22

thanks

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