## toxicsugar22 5 years ago 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

1. anonymous

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

2. toxicsugar22

yes

3. anonymous

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

4. anonymous

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

5. 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.

6. toxicsugar22

im guessing -3

7. toxicsugar22

is that right

8. anonymous

-3 is the slope of AC

9. toxicsugar22

ok

10. anonymous

So what is the slope perpendicular to that?

11. toxicsugar22

so what would be the equatin

12. toxicsugar22

1/-3

13. toxicsugar22

right

14. anonymous

No, negative reciprocal is perpendicular.

15. anonymous

so 1/3

16. 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?

17. toxicsugar22

y=1/3x+2

18. toxicsugar22

is that right

19. toxicsugar22

is thais right

20. anonymous

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

21. toxicsugar22

i think we put it in slope intecept form

22. anonymous

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

23. toxicsugar22

ok

24. toxicsugar22

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

25. anonymous

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

26. toxicsugar22

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

27. toxicsugar22

can u help me

28. anonymous

did you distribute the 1/3?

29. toxicsugar22

how do u do -4/3-2

30. anonymous

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

31. toxicsugar22

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

32. toxicsugar22

is that right then i subract 2 from both sides

33. anonymous

yes

34. toxicsugar22

then i get y=1/3x-3.3

35. toxicsugar22

is this write

36. anonymous

-3.33333 = -10/3

37. toxicsugar22

thanks you so much

38. 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.

39. toxicsugar22

can u help with this

40. anonymous

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

41. toxicsugar22

ok

42. toxicsugar22

but can u help me

43. 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.

44. toxicsugar22

i tried please can u help me

45. anonymous

what did you try?

46. toxicsugar22

i tried doing it but idid not get it

47. toxicsugar22

doing the pomble

48. toxicsugar22

can u help me

49. anonymous

what did you _do_ when you tried?

50. toxicsugar22

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

51. toxicsugar22

please can u help, I will be greatful to you

52. anonymous

what were you trying to find when you did that?

53. toxicsugar22

idk i thought that was how u do that

54. anonymous

do what?

55. toxicsugar22

the question

56. anonymous

Are you trying to find something?

57. toxicsugar22

yes the equation

58. anonymous

the equation of what?

59. 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

60. anonymous

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

61. toxicsugar22

i am finding it difficult please can u help me

62. anonymous

What are you trying to find here?

63. toxicsugar22

the equation i guess

64. anonymous

The equation of what?

65. toxicsugar22

the slope

66. toxicsugar22

the slope

67. anonymous

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

68. anonymous

What does that sentence mean?

69. toxicsugar22

i think it means that the line is touching line p

70. toxicsugar22

is that right

71. toxicsugar22

is this righ t

72. anonymous

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

73. toxicsugar22

idk

74. anonymous

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

75. toxicsugar22

is the slope -3/2

76. toxicsugar22

is it right

77. 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.

78. toxicsugar22

so it will be 2/3

79. toxicsugar22

is that right

80. anonymous

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

81. toxicsugar22

so we do (-1,-6)

82. toxicsugar22

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

83. toxicsugar22

is that right

84. anonymous

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

85. toxicsugar22

86. toxicsugar22

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

87. toxicsugar22

is this right

88. anonymous

yeah

89. toxicsugar22

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

90. anonymous

you can make it a fraction

91. toxicsugar22

how can u show me

92. anonymous

How many 3rds are there in 6 wholes?

93. toxicsugar22

so id it 20/3

94. toxicsugar22

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

95. toxicsugar22

i think that is right

96. toxicsugar22

i think that is right

97. 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

98. toxicsugar22

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

99. anonymous

no

100. 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

101. toxicsugar22

y=2/3x+20/3

102. anonymous

yes

103. toxicsugar22

thanks