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9.3-9.4 Reflections & Rotations

Author:Nicole Ianco, Jainesh Patel

Recall from yesterday....

Which term best describes a translation?

Select all that apply
  • A
  • B
  • C
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Reflection

In this section, students will be able to describe the effect of reflections on two dimensional figures using coordinates. For the reflection transformation, we will focus on two different line of reflections. Reflection over x-axis and y-axis. Below you are provided with three figures. The original pre-image (brown) and reflection over the y-axis (red) and over the x-axis (blue). Discover how figures are reflected over the x and y-axis by playing around with the original figure. Reshape the figure, move the figure around to learn. Have fun! Also think about mirrors, since we are going to work with coordinate points, what do you think will happen to the points when you reflect? Hint: Think about mirror, what happens when you raise your left arm, what do you see happening in a mirror?

Reflection

Question 1

Which term best describes a reflection?

Select all that apply
  • A
  • B
  • C
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Question 2

Rearrange the triangle so point A is at (4, 2). What is the point of reflection over the y-axis for point A? Now translate point A, 2 units up. What is the new point of reflection for over the y-axis for point A?

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Question 3

Relating to question 2, what difference do you notice about the coordinate points before and after the reflection over the y-axis?

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Question 4

Rearrange the triangle so point B is at (8, 4). What is the point of reflection over the x-axis for point B? Now translate point B, 2 units to the left. What is the new point of reflection for over the y-axis for point B?

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Question 5

Relating to question 4, what difference do you notice about the coordinate points before and after the reflection over the x-axis?

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Question 6

Which formula below best illustrates a reflection over the y-axis?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

Question 7

Which formula below best illustrates a reflection over the x-axis?

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  • A
  • B
  • C
  • D
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Question 8

Reflect the points below over the x-axis. What the new coordinate points A', B' and C'? A (1, 3) B (3, 4) C (-2, 5)

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Question 9

Reflect the points below over the y-axis. What the new coordinate points A', B' and C'? A (5, 2) B (-1, 6) C (3, -7)

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Question 10

A reflection over the x-axis makes the ________ opposite.

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  • A
  • B
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Question 11

A reflection over the y-axis makes the ________ opposite.

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  • A
  • B
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Rotation

In this section, students will be able to describe the effect of rotations on two dimensional figures using coordinates. For the rotation transformation, we will focus on two rotations. We will rotate our original figures 90 degrees counter-clockwise (brown figure) and 180 degrees (blue figure) about the origin (point O). Spend some time to play around with the original figure and see if you can notice the pattern with the change in coordinate points for the new figures of 90 and 180 degree rotations. Feel free to try different degrees for rotation, change it to counterclockwise to see how the figures and coordinates change. Have fun!

Rotation

Question 12

Which term best describes a rotation?

Select all that apply
  • A
  • B
  • C
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Question 13

A copy of a figure is called ________.

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  • A
  • B
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Question 14

Rigid transformations (translation, reflection, rotation) produce __________ figures.

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  • A
  • B
  • C
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Question 15

Rearrange the triangle so point A is at (4, 6), point B is at (8, 6) and point C is at (6, 2). a) What are the new coordinate points of A'2, B'2 and C'2 after a 90 degree counterclockwise (270 degree clockwise) rotation? b) What pattern you notice between the original points and the rotated points?

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Question 16

Rearrange the triangle so point A is at (4, 6), point B is at (8, 6) and point C is at (6, 2). a) What are the new coordinate points of A', B' and C' after a 180 degree rotation counter clockwise? b) What pattern you notice between the original points and the rotated points?

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Question 17

To rotate a figure 90 degrees counterclockwise, use this representation:

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  • A
  • B
  • C
  • D
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Question 18

To rotate a figure 180 degrees, use this representation:

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  • A
  • B
  • C
  • D
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Question 19

To rotate a figure 270 degrees counterclockwise , use this representation:

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  • A
  • B
  • C
  • D
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Question 20

Rotate the points below 180 degrees about the origin. What the new coordinate points A', B' and C'? A (-2, 3) B (4, -1) C (-5, -2)

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Question 21

Rotate the points below 90 degrees counterclockwise about the origin. What the new coordinate points A', B' and C'? A (4, 4) B (2, -1) C (-2, 3)

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Reflection over y=x and y=-x

Question 22

Triangle ABC is reflected over the line y=x. Write down the coordinates for A, B, and C and then the coordinates for A', B', and C'. What do you notice about how the coordinates change?

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Question 23

Which formula below best illustrates a reflection over the line y=x?

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  • A
  • B
  • C
  • D
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Question 24

Triangle ABC is reflected over the line y=-x. Write down the coordinates for A, B, and C and then the coordinates for A'1, B'1, and C'1. What do you notice about how the coordinates change?

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Question 25

Which formula below best illustrates a reflection over the line y= -x?

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  • A
  • B
  • C
  • D
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Once complete #1-25

Get a notes sheet from teacher. Copy in the coordinate notations from the corresponding slides above onto your paper then answer the questions that follow.

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