Graph the Pre-Image ABCD A(0,3), B(2,7), C(5,8) and D (4,5)

Question

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.

Answer 1

Here is a picture of the pre-image ABCD:

```
C(5,8)
|
|
B(2,7)------D(4,5)
|
|
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)
|
|
B'(-1,2)-----D'(1,0)
|
|
A'(-3,-2)
```

Answer 2

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

Answer 3

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)