toxicsugar22
  • toxicsugar22
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
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Do you recall the formula for the slope of a line given 2 points on the line?
toxicsugar22
  • toxicsugar22
yes
anonymous
  • anonymous
So use it to find the slope of the side AC.

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More answers

anonymous
  • anonymous
Once you have that you can find the perpendicular slope by taking the negative reciprocal
anonymous
  • 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
  • toxicsugar22
im guessing -3
toxicsugar22
  • toxicsugar22
is that right
anonymous
  • anonymous
-3 is the slope of AC
toxicsugar22
  • toxicsugar22
ok
anonymous
  • anonymous
So what is the slope perpendicular to that?
toxicsugar22
  • toxicsugar22
so what would be the equatin
toxicsugar22
  • toxicsugar22
1/-3
toxicsugar22
  • toxicsugar22
right
anonymous
  • anonymous
No, negative reciprocal is perpendicular.
anonymous
  • anonymous
so 1/3
anonymous
  • 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
  • toxicsugar22
y=1/3x+2
toxicsugar22
  • toxicsugar22
is that right
toxicsugar22
  • toxicsugar22
is thais right
anonymous
  • anonymous
I don't think so. It should be \(y+2 = \frac{1}{3}(x-4)\)
toxicsugar22
  • toxicsugar22
i think we put it in slope intecept form
anonymous
  • anonymous
sure, but I don't think if you do you'll get the answer you had before
toxicsugar22
  • toxicsugar22
ok
toxicsugar22
  • toxicsugar22
vut can u help me get me put that in slope inetcept form
anonymous
  • anonymous
Well start by distributing the 1/3, then subtract 2 from both sides
toxicsugar22
  • toxicsugar22
y+2=1/3(x-4) can u help me put tis in slpo intecept orm
toxicsugar22
  • toxicsugar22
can u help me
anonymous
  • anonymous
did you distribute the 1/3?
toxicsugar22
  • toxicsugar22
how do u do -4/3-2
anonymous
  • anonymous
convert -2 into an improper fraction (with a 3 in the denominator)
toxicsugar22
  • toxicsugar22
i got y+2=1/3x-4/3
toxicsugar22
  • toxicsugar22
is that right then i subract 2 from both sides
anonymous
  • anonymous
yes
toxicsugar22
  • toxicsugar22
then i get y=1/3x-3.3
toxicsugar22
  • toxicsugar22
is this write
anonymous
  • anonymous
-3.33333 = -10/3
toxicsugar22
  • toxicsugar22
thanks you so much
toxicsugar22
  • 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
  • toxicsugar22
can u help with this
anonymous
  • anonymous
umm.. it's pretty nearly the same problem, just with different numbers
toxicsugar22
  • toxicsugar22
ok
toxicsugar22
  • toxicsugar22
but can u help me
anonymous
  • 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
  • toxicsugar22
i tried please can u help me
anonymous
  • anonymous
what did you try?
toxicsugar22
  • toxicsugar22
i tried doing it but idid not get it
toxicsugar22
  • toxicsugar22
doing the pomble
toxicsugar22
  • toxicsugar22
can u help me
anonymous
  • anonymous
what did you _do_ when you tried?
toxicsugar22
  • toxicsugar22
idid (2,4) and (- 1and 6) and added the x and y
toxicsugar22
  • toxicsugar22
please can u help, I will be greatful to you
anonymous
  • anonymous
what were you trying to find when you did that?
toxicsugar22
  • toxicsugar22
idk i thought that was how u do that
anonymous
  • anonymous
do what?
toxicsugar22
  • toxicsugar22
the question
anonymous
  • anonymous
Are you trying to find something?
toxicsugar22
  • toxicsugar22
yes the equation
anonymous
  • anonymous
the equation of what?
toxicsugar22
  • 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
  • anonymous
I know what the problem says, I'm asking you what you think. You do think right? ;)
toxicsugar22
  • toxicsugar22
i am finding it difficult please can u help me
anonymous
  • anonymous
What are you trying to find here?
toxicsugar22
  • toxicsugar22
the equation i guess
anonymous
  • anonymous
The equation of what?
toxicsugar22
  • toxicsugar22
the slope
toxicsugar22
  • toxicsugar22
the slope
anonymous
  • anonymous
"Find the equation of the line tangent to the circle at the point P"
anonymous
  • anonymous
What does that sentence mean?
toxicsugar22
  • toxicsugar22
i think it means that the line is touching line p
toxicsugar22
  • toxicsugar22
is that right
toxicsugar22
  • toxicsugar22
is this righ t
anonymous
  • anonymous
The line is touching the point P that's on the circle, but what else do you know about it?
toxicsugar22
  • toxicsugar22
idk
anonymous
  • anonymous
well, specifically how does it relate to the radius of the circle through the point P?
toxicsugar22
  • toxicsugar22
is the slope -3/2
toxicsugar22
  • toxicsugar22
is it right
anonymous
  • 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
  • toxicsugar22
so it will be 2/3
toxicsugar22
  • toxicsugar22
is that right
anonymous
  • anonymous
that is the slope. now use the point p to find the equation like we did before
toxicsugar22
  • toxicsugar22
so we do (-1,-6)
toxicsugar22
  • toxicsugar22
so it would be y+6=2/3(x+1)
toxicsugar22
  • toxicsugar22
is that right
anonymous
  • anonymous
I thought P was (-1,6), so it would be y-6 = 2/3(x+1)
toxicsugar22
  • toxicsugar22
oh yeah sorry your right
toxicsugar22
  • toxicsugar22
if i put it in slope intecept orm it would be y=2/3x+6.67
toxicsugar22
  • toxicsugar22
is this right
anonymous
  • anonymous
yeah
toxicsugar22
  • toxicsugar22
but is the 6.67 right or can i put it in a fraction
anonymous
  • anonymous
you can make it a fraction
toxicsugar22
  • toxicsugar22
how can u show me
anonymous
  • anonymous
How many 3rds are there in 6 wholes?
toxicsugar22
  • toxicsugar22
so id it 20/3
toxicsugar22
  • toxicsugar22
wait i think we messed up it would be y+6=2/3(X-1)
toxicsugar22
  • toxicsugar22
i think that is right
toxicsugar22
  • toxicsugar22
i think that is right
anonymous
  • 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
  • toxicsugar22
so would it be y=2/3x+3/20
anonymous
  • anonymous
no
anonymous
  • 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
  • toxicsugar22
y=2/3x+20/3
anonymous
  • anonymous
yes
toxicsugar22
  • toxicsugar22
thanks

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