Question
Plot the image of quadrilateral
under a reflection across line
.
Hint #11 / 4
A reflection moves a point perpendicularly across a line, so that the is the same distance from the line as the , but on the other side.
Point R is reflected across a line to form point R prime. Segment R R prime is perpendicular to the line.
In other words, the line of reflection is the perpendicular bisector between any pair of corresponding points in the image and the pre-image.
Hint #22 / 4
Since line
is horizontal, the reflection will move each point of quadrilateral
vertically across the line of reflection.
For example, point
is
unit below line
, so
will be
unit above
.
A coordinate plane. The x- and y-axes both scale by one. A horizontal line is labeled l. Quadrilateral A B C D has point A two units away from the line on the top side, point B is on the line, point C is four units away from the bottom of the line, and point D is one unit away from the bottom of the line. A dashed arrow points at both point D prime at which is one unit away on the top side of the line and point D.
Hint #33 / 4
We can reflect each of the other vertices in the same way.
A coordinate plane. The x- and y-axes both scale by one. A horizontal line is labeled l. Quadrilateral A B C D has point A two units away from the line on the top side, point B is on the line, point C is four units away from the bottom of the line, and point D is one unit away from the bottom of the line. A dashed arrow points at both point D prime at which is one unit away on the top side of the line and point D. A dashed arrow points at both point C prime at which is four units away on the top side of the line and point C. point B prime is on the line at the same position of point B. A dashed arrow points at both point A prime at which is two units away on the bottom side of the line and point A.
We note that points
and
are in the same place because
was on the line of reflection.
Hint #44 / 4
This is the image of quadrilateral
under the reflection.
A coordinate plane. The x- and y-axes both scale by one. A horizontal line is labeled l. Quadrilateral A B C D has point A two units away from the line on the top side, point B is on the line, point C is four units away from the bottom of the line, and point D is one unit away from the bottom of the line. Quadrilateral A prime B prime C prime D prime is a reflection of Qudrilateral A B C D across the horizontal line withs point D prime at one unit away on the top side of the line point C prime at four units away on the top side of the line, point B prime on the line at the same position of point B, and point A prime at which is two units away on the bottom side of the line.
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under a reflection across line
.
Hint #11 / 4
A reflection moves a point perpendicularly across a line, so that the is the same distance from the line as the , but on the other side.
Point R is reflected across a line to form point R prime. Segment R R prime is perpendicular to the line.
In other words, the line of reflection is the perpendicular bisector between any pair of corresponding points in the image and the pre-image.
Hint #22 / 4
Since line
is horizontal, the reflection will move each point of quadrilateral
vertically across the line of reflection.
For example, point
is
unit below line
, so
will be
unit above
.
A coordinate plane. The x- and y-axes both scale by one. A horizontal line is labeled l. Quadrilateral A B C D has point A two units away from the line on the top side, point B is on the line, point C is four units away from the bottom of the line, and point D is one unit away from the bottom of the line. A dashed arrow points at both point D prime at which is one unit away on the top side of the line and point D.
Hint #33 / 4
We can reflect each of the other vertices in the same way.
A coordinate plane. The x- and y-axes both scale by one. A horizontal line is labeled l. Quadrilateral A B C D has point A two units away from the line on the top side, point B is on the line, point C is four units away from the bottom of the line, and point D is one unit away from the bottom of the line. A dashed arrow points at both point D prime at which is one unit away on the top side of the line and point D. A dashed arrow points at both point C prime at which is four units away on the top side of the line and point C. point B prime is on the line at the same position of point B. A dashed arrow points at both point A prime at which is two units away on the bottom side of the line and point A.
We note that points
and
are in the same place because
was on the line of reflection.
Hint #44 / 4
This is the image of quadrilateral
under the reflection.
A coordinate plane. The x- and y-axes both scale by one. A horizontal line is labeled l. Quadrilateral A B C D has point A two units away from the line on the top side, point B is on the line, point C is four units away from the bottom of the line, and point D is one unit away from the bottom of the line. Quadrilateral A prime B prime C prime D prime is a reflection of Qudrilateral A B C D across the horizontal line withs point D prime at one unit away on the top side of the line point C prime at four units away on the top side of the line, point B prime on the line at the same position of point B, and point A prime at which is two units away on the bottom side of the line.
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Answers
GPT-4o mini
To reflect the quadrilateral ABCD across a horizontal line (let's call it line \( l \)), we need to analyze the positions of the vertices A, B, C, and D relative to line \( l \) and then determine the positions of their corresponding reflected points A', B', C', and D'.
Let's say the line \( l \) is positioned at \( y = k \) on the coordinate plane. The points are described as follows:
- Point A is 2 units above line \( l \).
- Point B is on line \( l \) (meaning its y-coordinate is \( k \)).
- Point C is 4 units below line \( l \) (so its y-coordinate is \( k - 4 \)).
- Point D is 1 unit below line \( l \) (so its y-coordinate is \( k - 1 \)).
To find the coordinates of the reflected points:
1. **Point A**: Since A is 2 units above the line \( l \) (y-coordinate \( k + 2 \)), its reflection A' will be 2 units below line \( l\):
- \( A' \) will be at \( (x_A, k - 2) \).
2. **Point B**: Point B is on line \( l\) (y-coordinate \( k \)), so its reflection B' will remain the same:
- \( B' = B \) (at \( (x_B, k) \)).
3. **Point C**: Since C is 4 units below line \( l \) (y-coordinate \( k - 4 \)), its reflection C' will be 4 units above line \( l\):
- \( C' \) will be at \( (x_C, k + 4) \).
4. **Point D**: D is 1 unit below line \( l \) (y-coordinate \( k - 1 \)), so its reflection D' will be 1 unit above line \( l\):
- \( D' \) will be at \( (x_D, k + 1) \).
Now, summarizing the final coordinates for the reflected quadrilateral \( A'B'C'D' \):
- \( A' = (x_A, k - 2) \)
- \( B' = (x_B, k) \)
- \( C' = (x_C, k + 4) \)
- \( D' = (x_D, k + 1) \)
This gives you the reflected image of quadrilateral ABCD across the line \( l \). You can now plot these points on the coordinate plane to visualize the reflected quadrilateral \( A'B'C'D' \).
Let's say the line \( l \) is positioned at \( y = k \) on the coordinate plane. The points are described as follows:
- Point A is 2 units above line \( l \).
- Point B is on line \( l \) (meaning its y-coordinate is \( k \)).
- Point C is 4 units below line \( l \) (so its y-coordinate is \( k - 4 \)).
- Point D is 1 unit below line \( l \) (so its y-coordinate is \( k - 1 \)).
To find the coordinates of the reflected points:
1. **Point A**: Since A is 2 units above the line \( l \) (y-coordinate \( k + 2 \)), its reflection A' will be 2 units below line \( l\):
- \( A' \) will be at \( (x_A, k - 2) \).
2. **Point B**: Point B is on line \( l\) (y-coordinate \( k \)), so its reflection B' will remain the same:
- \( B' = B \) (at \( (x_B, k) \)).
3. **Point C**: Since C is 4 units below line \( l \) (y-coordinate \( k - 4 \)), its reflection C' will be 4 units above line \( l\):
- \( C' \) will be at \( (x_C, k + 4) \).
4. **Point D**: D is 1 unit below line \( l \) (y-coordinate \( k - 1 \)), so its reflection D' will be 1 unit above line \( l\):
- \( D' \) will be at \( (x_D, k + 1) \).
Now, summarizing the final coordinates for the reflected quadrilateral \( A'B'C'D' \):
- \( A' = (x_A, k - 2) \)
- \( B' = (x_B, k) \)
- \( C' = (x_C, k + 4) \)
- \( D' = (x_D, k + 1) \)
This gives you the reflected image of quadrilateral ABCD across the line \( l \). You can now plot these points on the coordinate plane to visualize the reflected quadrilateral \( A'B'C'D' \).