Reflections

Show your work for each problem.

1.
What is the rule for reflecting a point across the x-axis?
1. a)
2. b)
3. c)
4. d)
Answer:
When reflecting across the x-axis, points flip vertically. The x-coordinate stays the same, but the y-coordinate becomes its opposite: .
2.
Reflect the point across the x-axis. What is the y-coordinate of the image?
Answer: -7
Reflecting across the x-axis gives . The y-coordinate changes from to .
3.
Reflect the point across the y-axis. What is the x-coordinate of the image?
Answer: 5
Reflecting across the y-axis gives . The x-coordinate changes from to .
4.
A point is reflected across the y-axis. What are the coordinates of ?
1. a)
2. b)
3. c)
4. d)
Answer:
For y-axis reflection: . So .
5.
Which statement is TRUE about reflections?
1. a)The image is rotated
2. b)The image is congruent to the pre-image
3. c)The size of the image changes
4. d)The image is smaller than the pre-image
Answer: The image is congruent to the pre-image
Reflections are rigid transformations. They create a mirror image that is exactly the same size and shape as the original - the figures are congruent.
6.
Reflect the point across the x-axis to get .
Answer: (-3, -4)
1. What is the rule for x-axis reflection? (x, -y)
2. What is the x-coordinate of A? -3
3. Does the x-coordinate change? no
4. What is (the opposite of 4)? -4
5. What are the coordinates of ? (-3, -4)
7.
Reflect the point across the y-axis. Write the image as an ordered pair (x, y).
Answer: (-6, -2)
Y-axis reflection: . So .
8.
What is the rule for reflecting a point across the line ?
1. a)
2. b)
3. c)
4. d)
Answer:
When reflecting across , the x and y coordinates swap: . For example, becomes .
9.
A triangle has vertex . Reflect vertex across the y-axis to find .
Answer: (-2, 5)
1. What is the reflection rule for the y-axis? (-x, y)
2. What is the x-coordinate of A? 2
3. What is the opposite of 2? -2
4. Does the y-coordinate change? no
5. What are the coordinates of ? (-2, 5)
10.
Reflect the point across the line . Write the image as (x, y).
Answer: (1, 4)
Reflecting across : swap coordinates to get .
11.
A point is reflected across the y-axis. What is the image?
1. a)
2. b)
3. c)
4. d)
Answer:
The point is on the y-axis (since ). When a point is on the line of reflection, it stays in the same place. So the image is .
12.
Reflect the point across the line .
Answer: (3, -5)
1. What is the rule for reflecting across ? (y, x)
2. What is the x-coordinate of the original point? -5
3. What is the y-coordinate of the original point? 3
4. After swapping, what is the new x-coordinate? 3
5. After swapping, what is the new y-coordinate? -5
6. What are the final coordinates? (3, -5)
13.
A point is reflected first across the x-axis, then across the y-axis. Find the final image.
Answer: (-4, 2)
1. First, reflect across the x-axis. What is the result? (4, 2)
2. Now reflect across the y-axis. What is the result? (-4, 2)
3. Compare the final image to the original. Both coordinates are? negated
14.
Triangle has vertices , , and . If the triangle is reflected across the x-axis, what are the coordinates of ?
Answer: (2, -5)
For x-axis reflection: . So .
15.
If a point is reflected across the x-axis to get , and then is reflected across the x-axis again, where does the final image land?
1. a)At the origin
2. b)Back at the original point
3. c)At a different location
4. d)On the y-axis
Answer: Back at the original point
Reflecting twice across the same line brings you back to where you started. If .
16.
A rectangle has vertices at , , , and . Find the vertices of the rectangle after reflecting across the y-axis.
Answer: A'(-1, 1), B'(-5, 1), C'(-5, 3), D'(-1, 3)
1. What is the y-axis reflection rule? (-x, y)
2. Reflect . What is ? (-1, 1)
3. Reflect . What is ? (-5, 1)
4. Reflect . What is ? (-5, 3)
5. Reflect . What is ? (-1, 3)