## hali12 3 years ago In the figure below, all the points are evenly spaced along the line. What is the coordinate of point L?

1. hali12

2. hali12

@jim_thompson5910 can u pleasse help me with a few questions?

3. completeidiot

8+x=L L+x=26 substitute (8+x)+x=26 x is the same for both expressions because the points are equally spaced solve for x, then solve for L

4. hali12

uhhh...

5. jim_thompson5910

the points are evenly spaced, so L is the same distance away from both points B and E

6. jim_thompson5910

So L is the midpoint of BE

7. jim_thompson5910

do you see this?

8. hali12

yea

9. jim_thompson5910

so we can say (B+E)/2 = L or basically take the value of B, add it to E, then divide by 2 to get L

10. jim_thompson5910

what does that give you?

11. hali12

17

12. jim_thompson5910

perfect

13. hali12

sweet

14. hali12

can we do number 4 please?

15. jim_thompson5910

what is the distance from point T to point E

16. hali12

15

17. jim_thompson5910

good, now what's 2/3 of 15?

18. hali12

10

19. jim_thompson5910

so the distance from point T to point P is 10 units (since P is 2/3 of the way from T to E)

20. jim_thompson5910

21. hali12

-4

22. jim_thompson5910

good

23. hali12

thanks, im going to post more, maybe u can help me?

24. jim_thompson5910

alright go for it

25. hali12

26. jim_thompson5910

tell me what you get for each

27. hali12

1) true 2) True 3) true 4) true 5) False

28. jim_thompson5910

did you mean #5 through #9?

29. jim_thompson5910

and not #1 through #5

30. hali12

yea

31. jim_thompson5910

how did you get #3 to be true?

32. hali12

cause the line goes through the AM

33. jim_thompson5910

does it? take a very close look at it

34. jim_thompson5910

try to rotate it in your mind

35. jim_thompson5910

better yet, get a piece of paper, label it and try it out

36. hali12

k

37. hali12

ohhhhhh i see its like putting a pencil through a peice of paper

38. jim_thompson5910

exactly, so do they intersect?

39. hali12

no

40. hali12

are the rest correct?

41. jim_thompson5910

good

42. jim_thompson5910

why is the last one false?

43. hali12

idk, i wanted to put true, but something was teling me to put false

44. jim_thompson5910

do E, D and C all lie on the same line?

45. hali12

yes

46. jim_thompson5910

so they are collinear by the very definition of collinear

47. jim_thompson5910

points are collinear if they all lie on the same straight line

48. jim_thompson5910

Example |dw:1343852694256:dw|

49. jim_thompson5910

Example of non-collinear points |dw:1343852731003:dw|

50. jim_thompson5910

Notice how there is no way to draw a straight line through all of the points, so those points are noncollinear

51. hali12

ohhh

52. jim_thompson5910

make sense?

53. hali12

ya

54. jim_thompson5910

ok great

55. hali12

56. jim_thompson5910

again tell me what you get

57. hali12

p?

58. jim_thompson5910

for #12 right?

59. hali12

ya

60. jim_thompson5910

yes, P is coplanar with T, R and Q

61. jim_thompson5910

they all lie in the same plane (the back face)

62. hali12

13) rt?

63. jim_thompson5910

no, what do the back face and the bottom face have in common (where do they intersect)?

64. hali12

pt?

65. jim_thompson5910

you got it

66. jim_thompson5910

that bottom edge in the back is what they have in common

67. hali12

68. hali12

#14) 5?

69. jim_thompson5910

#14 how many faces does the figure have?

70. hali12

2?

71. hali12

3

72. jim_thompson5910

think of a house

73. jim_thompson5910

how many walls does it have?

74. hali12

its the sides u can see right?

75. jim_thompson5910

and the sides that are hidden (because they are in the back)

76. jim_thompson5910

think of it rotating

77. hali12

4

78. jim_thompson5910

4 walls, good

79. jim_thompson5910

how many parts to the roof?

80. jim_thompson5910

flat parts

81. hali12

6

82. jim_thompson5910

6 flat parts to the roof? or 6 total so far?

83. hali12

total

84. jim_thompson5910

ok, then count in the floor

85. hali12

7

86. hali12

7

87. jim_thompson5910

yes

88. jim_thompson5910

there are 7 faces total

89. jim_thompson5910

so there are 7 planes

90. hali12

oh ok

91. jim_thompson5910

with any geometric solid, a "face" is also a plane

92. hali12

I

93. jim_thompson5910

?

94. hali12

number 15 is i ?

95. jim_thompson5910

points D, J and A all lie on the left wall (that's behind the front and right walls...so it's hidden from view)

96. hali12

f?

97. jim_thompson5910

what also lies on that left wall?

98. hali12

a,d,g,j,f,i

99. jim_thompson5910

i and f don't because they lie on the left rooftop

100. hali12

g

101. jim_thompson5910

yes, the answer to #15 is g

102. hali12

now for number 16 im confused

103. jim_thompson5910

draw a line from D to J

104. jim_thompson5910

which face does this line lie in?

105. hali12

106. jim_thompson5910

good

107. jim_thompson5910

another way to name JADG is JAD since 3 points are enough to make a plane

108. hali12

is 17 plane JIG?

109. hali12

i mean JGF

110. jim_thompson5910

yes, JIG is the same plane as JGF and they both work

111. jim_thompson5910

but JGF is the only listed answer, so it's JGF

112. hali12

number 18 "No answer is correct."?

113. jim_thompson5910

very good

114. jim_thompson5910

there is no face that has the line

115. hali12

sweet!

116. hali12

117. hali12

non-coplanar ( number 19)

118. jim_thompson5910

are you sure? look again (very closely)

119. hali12

collinear

120. jim_thompson5910

do they all lie on the same line?

121. hali12

no non-collinear

122. jim_thompson5910

good, so #19 is non-collinear

123. hali12

#20 non-coplanar

124. jim_thompson5910

yes, very good

125. jim_thompson5910

not all of those 3 points lie in the same plane/face

126. hali12

21 - non-coplanar?

127. jim_thompson5910

good, from 20, A, B and G are noncoplanar, so throwing in another point (whatever that new point may be) will not change this

128. hali12

22 - They don’t intersect.

129. jim_thompson5910

good

130. hali12

23 - collinear

131. jim_thompson5910

do they all lie on the same line?

132. hali12

no non-coplanar

133. jim_thompson5910

so they do NOT lie in the same plane?

134. hali12

no

135. jim_thompson5910

are you sure?

136. hali12

yes

137. jim_thompson5910

look again

138. hali12

yes they do, coplanar

139. jim_thompson5910

yes you are correct

140. hali12

24- collinear

141. jim_thompson5910

they all lie on the same line?

142. hali12

yes

143. jim_thompson5910

look again

144. hali12

no

145. jim_thompson5910

so not colllinear

146. jim_thompson5910

collinear*

147. hali12

non-collinear

148. jim_thompson5910

good

149. hali12

last one

150. hali12

non-coplanar

151. jim_thompson5910

correct

152. hali12

AWESOME , THANK YOU SO MUCH FOR TAKING TIME TO HELP ME OUT

153. jim_thompson5910

you're very welcome