## OpenSessame Group Title Find the image of P(–2, –1) after two reflections; first Ry=-5 and then Rx=1. A. (–2, –1) B. (–1, –6) C. (4, –9) D. (1, –5) one year ago one year ago

1. e.mccormick Group Title

So the Ry=-5 and Rx=1 are the lines you need to reflect across?

2. OpenSessame Group Title

Those are the reflections

3. e.mccormick Group Title

A reflection is usually over a line.... so I want to make sure that is the notation you are using.

4. OpenSessame Group Title

I think so...

5. e.mccormick Group Title

http://www.mathopenref.com/reflect.html Like it says there, "A transformation where each point in a shape appears at an equal distance on the opposite side of a given line - the line of reflection. " So, start by just doing a rough sketch. Does not need to be exact, but you need to find where the dot and line would be and how far the line is from the dot. If you can do that with math, great! But a sketch can help.

6. OpenSessame Group Title

Okay, but i dont understand what i have to do...

7. e.mccormick Group Title

Well, it needs to be an equal distance from the line on the other side of the line.

8. OpenSessame Group Title

Where did the line come from????

9. OpenSessame Group Title

You lost me..

10. e.mccormick Group Title

Ry=-5 $$\leftarrow$$ that is the line part.

11. e.mccormick Group Title

Let me show you an example.

12. OpenSessame Group Title

Okay...Just show me with this one

13. e.mccormick Group Title

If I work this that is me giving you an answer. If I work an example you can follow the process and answer your own homework. Lets say I take this random dot: |dw:1376455485961:dw| And lets say I have Ry=1, so the line where every Y is 1.

14. e.mccormick Group Title

|dw:1376455572591:dw|

15. OpenSessame Group Title

Well, im really lost man...So i wouldnt even get it

16. OpenSessame Group Title

That is an example already, im just doing a text review for before i take it. so it doesnt count

17. e.mccormick Group Title

The important measure is the distance from the dot to the line. |dw:1376455620753:dw| Because I need to put the reflection the SAME DISTANCE on the other side of the line.

18. e.mccormick Group Title

|dw:1376455677255:dw|

19. OpenSessame Group Title

Do the distance is the number in the equation?

20. OpenSessame Group Title

Let me try to do mine...one sec

21. e.mccormick Group Title

The distance is the measure from your point and the line.

22. e.mccormick Group Title

Yours is done twice.... so see what you get for the first step and I can check it. Then the second step.

23. OpenSessame Group Title

|dw:1376455841757:dw|

24. e.mccormick Group Title

OK, that is a good (-2,-1).

25. OpenSessame Group Title

|dw:1376455914360:dw|

26. OpenSessame Group Title

Now what do i do exactly?

27. e.mccormick Group Title

OK, so what is the measure of the distance between your dot and the line? |dw:1376456012468:dw|

28. OpenSessame Group Title

-3?

29. e.mccormick Group Title

Not quite. Tewo problems. This is change in y, not x, and distance is always positive.

30. OpenSessame Group Title

so 4?

31. e.mccormick Group Title

Yes. So your point is 4 above the line. That means the reflection must be 4 BELOW the line!

32. OpenSessame Group Title

so at -5?

33. OpenSessame Group Title

wait no....-4?

34. e.mccormick Group Title

The line is at -5. So 4 below -5.... or -5-4=?

35. e.mccormick Group Title

Above is +, below is -. Similarly, to the left of is -, to the right of is +. Has to do with the Cartesian (xy) plane rules.

36. OpenSessame Group Title

Ohhhh so -9?

37. e.mccormick Group Title

Yes. That means the X is the same and the Y is now -9. So, the point after 1 translation is at (-2,-9). |dw:1376456612998:dw|

38. e.mccormick Group Title

Now you have the line Rx=1 to do the second reflection over.

39. OpenSessame Group Title

okay:) i get it!

40. OpenSessame Group Title

|dw:1376456678313:dw|

41. OpenSessame Group Title

|dw:1376456695550:dw|

42. e.mccormick Group Title

So, how far this time?

43. OpenSessame Group Title

3?

44. e.mccormick Group Title

$$\large\ddot\smile$$

45. OpenSessame Group Title

so the point would me three to the right?

46. OpenSessame Group Title

so (4,-9)????

47. e.mccormick Group Title

Yes, 3 to the right of 1. And yep, that is it. (4,-9).

48. OpenSessame Group Title

wait im gonna see if it matches...

49. e.mccormick Group Title

Now, once you get good at the math, you should not need a sketch, but if yuou are ever in doubt, the rough sketch is there to help!

50. OpenSessame Group Title

Okay, the textbook just didnt really explain it

51. e.mccormick Group Title

The thing I think most people mes up here is the line.... because x=0 is the y axis, and y=0 is the x axis. So they give you a y line but you draw it the same way as the x axis and that can be confusing!

52. OpenSessame Group Title

yea, thats the right answer! thanks:)

53. OpenSessame Group Title

Can you help with some other questions that i dont get?

54. e.mccormick Group Title

Probably. I can explain it the same basic way I always do and hopefully it works like this and you get it!

55. OpenSessame Group Title

Okay, thanks:)

56. OpenSessame Group Title

What composition of rigid motions and a dilation maps EFGH to the dashed figure? https://study.ashworthcollege.edu/access/content/group/45b8c516-1008-46d7-aa1d-bb9b62c786ff/geometry_exam_9_files/mc020-1.jpg

57. e.mccormick Group Title

OK. Dilation is going to be the size change. The rigit motion will get it from one place to the other.

58. OpenSessame Group Title

Okay...

59. e.mccormick Group Title

It is probably easiest to do the dilation first. That will be some multiplication number. It is a ratio of the sides.

60. OpenSessame Group Title

Okay...

61. e.mccormick Group Title

For example, this would be a dialation by 3..... |dw:1376457753408:dw| So start by finding how long the sides of both rectangles are.

62. OpenSessame Group Title

63. e.mccormick Group Title

2x the size, so yah, a dialation of 2. I didn't do the rest yet, but that would probably do it.

64. OpenSessame Group Title

Really??? woooohoooo

65. e.mccormick Group Title

Hmmm.... -6.... is that enough on the translation?

66. OpenSessame Group Title

Idk...

67. e.mccormick Group Title

Well, lets look at this real quick: |dw:1376458028692:dw| Now you need to double the size.

68. OpenSessame Group Title

The dialation is times 2?

69. e.mccormick Group Title

|dw:1376458060944:dw| OK, that makes them reflections of each other.

70. e.mccormick Group Title

So now, one of two things needs to happne.... It either needs to be reflected over the x axis, OR, corner H needs to go all the way down to the bottom corner. |dw:1376458143764:dw|

71. OpenSessame Group Title

so its shifted down -6

72. e.mccormick Group Title

Well, is that 6? That bottom corner is at -9....

73. OpenSessame Group Title

-10?

74. e.mccormick Group Title

or -10, actually.... counted wrong.

75. e.mccormick Group Title

So it has to go from 2 above to -10 below... so....

76. OpenSessame Group Title

so uhm...It would be 11?

77. OpenSessame Group Title

12

78. e.mccormick Group Title

Yep! So 2D, T$$\langle 0,-12\rangle$$ is more like it.

79. OpenSessame Group Title

that isnt one of my options

80. e.mccormick Group Title

Hmmm.... AH.... OK... the dialaion is probably also changing the translation! $$2\langle 0,-6\rangle = \langle 0,-12\rangle$$

81. e.mccormick Group Title

So my bad. Looks like you did have it right.

82. OpenSessame Group Title

YUS:) thanks though!

83. OpenSessame Group Title

The hexagon GIKMPR and FJN are regular. The dashed line segments form 30° angles. What is r(240drg,0)(G)

84. OpenSessame Group Title
85. e.mccormick Group Title

Well, the good news is you should understand the why a bit better! By exploring these, it lets you understand the why of it all....

86. OpenSessame Group Title

okay!

87. e.mccormick Group Title

Hmmm..... I have not seen that form of question.... my geometry was a while back, and they have changed some of the things they do... Do you know what it is looking for, any terms? An angle?

88. OpenSessame Group Title

240 degrees

89. OpenSessame Group Title

Thats really all i understand...

90. e.mccormick Group Title

r is usually a radius.... but there is no distance....

91. OpenSessame Group Title

I think r is the point?

92. e.mccormick Group Title

Is it R and not r?

93. OpenSessame Group Title
94. OpenSessame Group Title

Thats the problem..

95. e.mccormick Group Title

hmmm..... Well, 240/30=8 segments.

96. OpenSessame Group Title

so 8 to the left or right?

97. e.mccormick Group Title

Well, if r is right... but that would be a guess on my part. Right 8 of G? I would need to see the reference to know they type of peoblem to get this one.

98. OpenSessame Group Title

So would it be K???

99. e.mccormick Group Title

I would only be guessing without the book and chapter.

100. OpenSessame Group Title

Okay...Well for me thats better then nothing!

101. OpenSessame Group Title

The vertices of a triangle are P(–8, 6), Q(1, –3), and R(–6, –3). Name the vertices of $R _{y=x}(PQR)$

102. e.mccormick Group Title

Is that a reflection over the y axis?

103. OpenSessame Group Title

I believe it is.

104. e.mccormick Group Title

AH HA! Found a reference! http://www.regentsprep.org/Regents/math/geometry/GT6/composition.htm

105. OpenSessame Group Title

You did??

106. OpenSessame Group Title

OOOOO

107. e.mccormick Group Title

The composition part does not matter here.... the $$R_y$$ part is reflection over the y axis!

108. OpenSessame Group Title

So just make it the other sign?

109. e.mccormick Group Title
110. OpenSessame Group Title

Would the first point be (-6,8)

111. OpenSessame Group Title

OHHHH!!! MAKES SENSE!

112. OpenSessame Group Title

so (6,-8)

113. e.mccormick Group Title

Amazing what finding a reference to the symbols can do!

114. OpenSessame Group Title

YEA! Thanks so much man!

115. OpenSessame Group Title

Write a sequence of rigid motions that maps ab and xy

116. OpenSessame Group Title
117. OpenSessame Group Title

LAST ONE AND I WILL UNDERSTAND GEOMETRY!

118. e.mccormick Group Title

That composition part also confirms what we talked about with the <0,-6> becoming <0,-12>. The SECOND part of the compositon happens first!

119. OpenSessame Group Title

the second part is (AB=XY)

120. e.mccormick Group Title

Are those seperate calculations for those two?

121. OpenSessame Group Title

The top doesnt matter just look at the lines

122. e.mccormick Group Title

Yah, well, then that is some sort of what? Rotation, reflection etc?

123. OpenSessame Group Title

Reflection?

124. e.mccormick Group Title

Remember that A is going to X and B is going to Y..... should be a huge clue.... YES! Some sort of reflection.

125. e.mccormick Group Title

So, you just need to find the line they are reflected over.

126. e.mccormick Group Title

It would be half way between them.

127. OpenSessame Group Title

0?

128. e.mccormick Group Title

Are they both the same distance from x=0?

129. OpenSessame Group Title

yES...

130. e.mccormick Group Title

Did you count the distance from 0 to X and 0 to A?

131. OpenSessame Group Title

no...

132. e.mccormick Group Title

Take a second look.... they are not the same.

133. OpenSessame Group Title

Oh...

134. e.mccormick Group Title

You want the line half way between. So take the distance between the two points and divide by 2. It will be that far to the left of the right most line, and right of the left most line.

135. OpenSessame Group Title

okay...