Question
A translation moves point V(–2, 3) to V prime (negative 2, 7). Which are true statements about the translation?
The point moves two units left and four units up.
The transformation rule is (x, y) right-arrow (x + 0, y + 4).
The transformation is a vertical translation.
The image is four units to the left of the pre-image.
The translation can be described as (x, y) right-arrow (x minus 2, y + 7).
The point moves two units left and four units up.
The transformation rule is (x, y) right-arrow (x + 0, y + 4).
The transformation is a vertical translation.
The image is four units to the left of the pre-image.
The translation can be described as (x, y) right-arrow (x minus 2, y + 7).
Answers
GPT-4o mini
Let's analyze the translation of point V(–2, 3) to V'(–2, 7).
1. **The point moves two units left and four units up.**
- This statement is **false**. The x-coordinate does not change (it stays at -2), so there is no movement left or right. The y-coordinate changes from 3 to 7, which is an upward movement of 4 units.
2. **The transformation rule is (x, y) right-arrow (x + 0, y + 4).**
- This statement is **true**. The x-coordinate remains the same (x + 0), and the y-coordinate increases by 4 (y + 4).
3. **The transformation is a vertical translation.**
- This statement is **true**. Since only the y-coordinate changes (it moves from 3 to 7) and the x-coordinate remains constant, it is a vertical translation.
4. **The image is four units to the left of the pre-image.**
- This statement is **false**. The point V' is not to the left of V; both points have the same x-coordinate.
5. **The translation can be described as (x, y) right-arrow (x minus 2, y + 7).**
- This statement is **false**. The translation does not involve subtracting 2 from x; instead, x remains the same, and y is increased by 4. The correct transformation would be (x, y) right-arrow (x + 0, y + 4) or simply (x, y) right-arrow (x, y + 4).
In summary:
- True statements: 2 and 3.
- False statements: 1, 4, and 5.
1. **The point moves two units left and four units up.**
- This statement is **false**. The x-coordinate does not change (it stays at -2), so there is no movement left or right. The y-coordinate changes from 3 to 7, which is an upward movement of 4 units.
2. **The transformation rule is (x, y) right-arrow (x + 0, y + 4).**
- This statement is **true**. The x-coordinate remains the same (x + 0), and the y-coordinate increases by 4 (y + 4).
3. **The transformation is a vertical translation.**
- This statement is **true**. Since only the y-coordinate changes (it moves from 3 to 7) and the x-coordinate remains constant, it is a vertical translation.
4. **The image is four units to the left of the pre-image.**
- This statement is **false**. The point V' is not to the left of V; both points have the same x-coordinate.
5. **The translation can be described as (x, y) right-arrow (x minus 2, y + 7).**
- This statement is **false**. The translation does not involve subtracting 2 from x; instead, x remains the same, and y is increased by 4. The correct transformation would be (x, y) right-arrow (x + 0, y + 4) or simply (x, y) right-arrow (x, y + 4).
In summary:
- True statements: 2 and 3.
- False statements: 1, 4, and 5.