Graph the Pre-Image ABCD A(0,3), B(2,7), C(5,8) and D (4,5)
Can you draw a picture for me, to give me a visual view of how it would look please that would really help. Then Translate the Pre-Image ABCD with the following translation rule: (x,y) —> (x-3, y-5) and name the Image vertices.
Here is a picture of the pre-image ABCD:
```
C(5,8)
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B(2,7)------D(4,5)
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A(0,3)
```
To translate the pre-image ABCD using the translation rule (x,y) —> (x-3, y-5), we will subtract 3 from the x-coordinate and subtract 5 from the y-coordinate of each vertex.
So the image vertices would be:
- A(0,3) -> A'(-3,-2)
- B(2,7) -> B'(-1,2)
- C(5,8) -> C'(2,3)
- D(4,5) -> D'(1,0)
Here is a picture of the translated image A'B'C'D':
```
C'(2,3)
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B'(-1,2)-----D'(1,0)
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A'(-3,-2)
```
a. To reflect the pre-image ABCD across the line y=2, we need to keep the x-coordinates the same and change the sign of the y-coordinates. The line y=2 acts as a mirror, so the distance between the line and the corresponding point on either side will be the same.
So the image vertices would be:
- A(0,3) -> A(0,1)
- B(2,7) -> B(2,-3)
- C(5,8) -> C(5,-6)
- D(4,5) -> D(4,-3)
b. To reflect the pre-image ABCD across the Y-axis, we need to change the sign of the x-coordinates and keep the y-coordinates the same. The Y-axis acts as a mirror, so the distance between the Y-axis and the corresponding point on either side will be the same.
So the image vertices would be:
- A(0,3) -> A(0,3)
- B(2,7) -> B(-2,7)
- C(5,8) -> C(-5,8)
- D(4,5) -> D(-4,5)
Thank you, can you answer this with the information above
Reflect the Pre-Image ABCD with the following Reflections and name the Image vertices:
a. Across the line y=2 And also B. Across the Y axis
To graph the pre-image ABCD, you can simply plot the given points A(0,3), B(2,7), C(5,8), and D(4,5) on a coordinate plane.
Here's how to do it step by step:
1. Draw a set of coordinate axes on a sheet of graph paper or using a drawing program.
2. Locate the point A(0,3) on the graph. This means that point A is located at x=0 (horizontal axis) and y=3 (vertical axis). Mark this point.
3. Locate the point B(2,7) on the graph. Point B is at x=2 and y=7. Mark this point as well.
4. Locate the point C(5,8) on the graph. Point C is located at x=5 and y=8. Mark this point too.
5. Locate the point D(4,5) on the graph. Point D is at x=4 and y=5. Mark it also.
6. Finally, connect these points in order to form a quadrilateral.
Now, let's translate the pre-image ABCD using the given translation rule: (x,y) —> (x-3, y-5). This rule means that for each vertex of the pre-image, we will subtract 3 from its x-coordinate and subtract 5 from its y-coordinate to get the coordinates of the image vertices.
The new coordinates of the image vertices A', B', C', and D' will be:
A': (0-3, 3-5) -> (-3, -2)
B': (2-3, 7-5) -> (-1, 2)
C': (5-3, 8-5) -> (2, 3)
D': (4-3, 5-5) -> (1, 0)
To visualize this translation, you can take the pre-image ABCD that you previously graphed and simply move each vertex 3 units to the left and 5 units down. Label the new vertices as A', B', C', and D' using the above coordinates.
I hope this explanation helps to give you a visual understanding of how the pre-image ABCD would look and the translated image ABCD'.