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,-1), D'(10,5)
A'(2,7), B'(5,9), C'(6,-1), D'(5,5)
A'(7,1), B'(10,4), C'(12,1), D'(10,1)
A'(-7,-7), B'(-10,-9), C'(-12,1), D'(-10,-5)

Answer 1

To translate quadrilateral ABCD by 2 units to the right and 4 units up, we 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 (the original coordinates are not provided; we'll just consider the changes):

- A → A' = (x_A + 2, y_A + 4)
- B → B' = (x_B + 2, y_B + 4)
- C → C' = (x_C + 2, y_C + 4)
- D → D' = (x_D + 2, y_D + 4)

Now, we analyze each option to find which one represents this translation.

1. **A'(7,7), B'(10,9), C'(12,-1), D'(10,5)**
- This could be valid depending on the original coordinates, but we cannot confirm without knowing the original A, B, C, D.

2. **A'(2,7), B'(5,9), C'(6,-1), D'(5,5)**
- Similar to the above, this could be valid.

3. **A'(7,1), B'(10,4), C'(12,1), D'(10,1)**
- Again, could be valid but remains unconfirmed.

4. **A'(-7,-7), B'(-10,-9), C'(-12,1), D'(-10,-5)**
- This cannot be valid since the coordinates have moved in the negative direction, which does not match the required translation of 2 units right and 4 units up.

Since we don't have the original coordinates, it is impossible to determine which of the new coordinates are the result of the correct translation. However, by the nature of translations, only the outputs that remain in the positive or unchanged quadrants should be considered, ruling out option 4.

From the specifics given, we cannot select a definitive answer without the original coordinates. If you can provide those coordinates for a sake of analysis, I would help check which ones match the right translations.