Question

Jarvis wants to translate rectangle ABDC horizontally by −4 and vertically by +3 to produce rectangle A′B′D′C′ . What will be the coordinates of C′ after Jarvis completes this translation?
Answer
The coordinates for point C' is, (-5,1)
Answer
C is, (-5,1) So, what would be C' coordinates?
Answered by GPT-4o mini
To find the coordinates of point C' after translating rectangle ABDC, we need to start with the coordinates of point C. However, you didn't provide the original coordinates of point C. Assuming the coordinates of point C are \( (x, y) \), we would perform the translations as follows:

1. **Horizontal translation by -4**: This means we will subtract 4 from the x-coordinate.
2. **Vertical translation by +3**: This means we will add 3 to the y-coordinate.

Therefore, the new coordinates for point C' can be calculated using the following formulas:

\[
x' = x - 4
\]
\[
y' = y + 3
\]

Consequently, the new coordinates of C' would be \( (x - 4, y + 3) \).

If you provide the specific coordinates for point C, I can give you the exact coordinates for point C'.
Answered by GPT-4o mini
Given the coordinates of point \( C' \) as \( (-5, 1) \), we can assume that this point is the result of applying the translation to point \( C \).

To find the original coordinates of point \( C \) (let's denote them as \( (x, y) \)), we can reverse the translation. The translation applied was:

1. Horizontal translation by -4 (subtracting 4 from the x-coordinate)
2. Vertical translation by +3 (adding 3 to the y-coordinate)

To reverse these translations, we can do the following:

1. For the x-coordinate:
\[
x = -5 + 4 = -1
\]

2. For the y-coordinate:
\[
y = 1 - 3 = -2
\]

Thus, the original coordinates of point \( C \) are \( (-1, -2) \).

**Summary:**
- After the translation, point \( C' \) is at \( (-5,1) \).
- The original point \( C \) before translation was at \( (-1,-2) \).
Answered by GPT-4o mini
If the coordinates of point \( C \) are \( (-5, 1) \) and we need to perform the following translations:

- Horizontal translation by -4 (subtract 4 from the x-coordinate)
- Vertical translation by +3 (add 3 to the y-coordinate)

We can calculate the new coordinates \( C' \) as follows:

1. **Horizontal translation**:
\[
x' = -5 - 4 = -9
\]

2. **Vertical translation**:
\[
y' = 1 + 3 = 4
\]

Therefore, the coordinates of point \( C' \) after the translation will be \( (-9, 4) \).