Question

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

Answer 1

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

Answer 2

yes

Answer 3

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

Answer 4

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

Answer 5

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.

Answer 6

im guessing -3

Answer 7

is that right

Answer 8

-3 is the slope of AC

Answer 9

ok

Answer 10

So what is the slope perpendicular to that?

Answer 11

so what would be the equatin

Answer 12

1/-3

Answer 13

right

Answer 14

No, negative reciprocal is perpendicular.

Answer 15

so 1/3

Answer 16

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?

Answer 17

y=1/3x+2

Answer 18

is that right

Answer 19

is thais right

Answer 20

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

Answer 21

i think we put it in slope intecept form

Answer 22

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

Answer 23

ok

Answer 24

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

Answer 25

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

Answer 26

y+2=1/3(x-4)

can u help me put tis in slpo intecept orm

Answer 27

can u help me

Answer 28

did you distribute the 1/3?

Answer 29

how do u do -4/3-2

Answer 30

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

Answer 31

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

Answer 32

is that right then i subract 2 from both sides

Answer 33

yes

Answer 34

then i get y=1/3x-3.3

Answer 35

is this write

Answer 36

-3.33333 = -10/3

Answer 37

thanks you so much

Answer 38

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.

Answer 39

can u help with this

Answer 40

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

Answer 41

ok

Answer 42

but can u help me

Answer 43

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.

Answer 44

i tried please can u help me

Answer 45

what did you try?

Answer 46

i tried doing it but idid not get it

Answer 47

doing the pomble

Answer 48

can u help me

Answer 49

what did you _do_ when you tried?

Answer 50

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

Answer 51

please can u help, I will be greatful to you

Answer 52

what were you trying to find when you did that?

Answer 53

idk i thought that was how u do that

Answer 54

do what?

Answer 55

the question

Answer 56

Are you trying to find something?

Answer 57

yes the equation

Answer 58

the equation of what?

Answer 59

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

Answer 60

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

Answer 61

i am finding it difficult please can u help me

Answer 62

What are you trying to find here?

Answer 63

the equation i guess

Answer 64

The equation of what?

Answer 65

the slope

Answer 66

the slope

Answer 67

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

Answer 68

What does that sentence mean?

Answer 69

i think it means that the line is touching line p

Answer 70

is that right

Answer 71

is this righ t

Answer 72

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

Answer 73

idk

Answer 74

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

Answer 75

is the slope -3/2

Answer 76

is it right

Answer 77

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.

Answer 78

so it will be 2/3

Answer 79

is that right

Answer 80

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

Answer 81

so we do (-1,-6)

Answer 82

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

Answer 83

is that right

Answer 84

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

Answer 85

oh yeah sorry your right

Answer 86

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

Answer 87

is this right

Answer 88

yeah

Answer 89

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

Answer 90

you can make it a fraction

Answer 91

how can u show me

Answer 92

How many 3rds are there in 6 wholes?

Answer 93

so id it 20/3

Answer 94

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

Answer 95

i think that is right

Answer 96

i think that is right

Answer 97

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

Answer 98

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