Question

Translate quadrilateral ABCD by 2 units to the right and 4 units up. Which of the following are the coordinates of new quadrilateral A'B'C' D'?
(1 point)
• A' (7, 7). B'(10,9). C' (12, 7). D' (10, 5)
O A' (7, —1), B' (10, 1), C'(12, -1). D'(10, —3)
• A' (3, -1), B' (6, 1), C'(8, -1). D' (6, -3)
• A' (3, 7). B' (6, 9). C' (8, 7). D' (6, 5)

Answer 1

To translate quadrilateral ABCD by 2 units to the right and 4 units up, you need to add 2 to the x-coordinates and 4 to the y-coordinates of each vertex.

Let's denote the original coordinates of points A, B, C, and D as follows:

- A(x1, y1)
- B(x2, y2)
- C(x3, y3)
- D(x4, y4)

After the translation, the new coordinates (A', B', C', D') would be:

- A' = (x1 + 2, y1 + 4)
- B' = (x2 + 2, y2 + 4)
- C' = (x3 + 2, y3 + 4)
- D' = (x4 + 2, y4 + 4)

Now, let's analyze the options you provided, but it requires the original coordinates of the points A, B, C, and D to know if any of them are correct. However, if we assume some generic values for the original coordinates, let's check the options you've provided mathematically based on the translation rule.

**Assuming the original coordinates were (x, y):**
- A' = (x + 2, y + 4)
- B' = (x + 2, y + 4)
- C' = (x + 2, y + 4)
- D' = (x + 2, y + 4)

To find the valid new coordinates after applying the translation, let's go through the answer choices provided to see if any of them conform to this translation logic, without actual values for A, B, C, and D.

However, without the original coordinates of A, B, C, and D, it's not possible to determine which of the choices are valid. If you can provide the original coordinates, I can calculate the new ones for you. Alternatively, you can check for each option if they represent the transformation correctly by back-calculating to see if they could yield valid (x, y) pairs before the transformation.

Let me know if you have the original coordinates or if you need further assistance!