Question
A translation moves point V(–2, 3) to V prime (negative 2, 7). Which are true statements about the translation?
A. The point moves two units left and four units up.
B. The transformation rule is (x, y) right-arrow (x + 0, y + 4).
C. The transformation is a vertical translation.
D. The image is four units to the left of the pre-image.
E. The translation can be described as (x, y) right-arrow (x minus 2, y + 7).
A. The point moves two units left and four units up.
B. The transformation rule is (x, y) right-arrow (x + 0, y + 4).
C. The transformation is a vertical translation.
D. The image is four units to the left of the pre-image.
E. The translation can be described as (x, y) right-arrow (x minus 2, y + 7).
Answers
GPT-4o mini
To analyze the translation of point V(–2, 3) to V prime (–2, 7), we can look at how the x-coordinate and y-coordinate have changed.
1. The x-coordinate of V is -2 and the x-coordinate of V prime is also -2. This means the point did not move left or right horizontally.
2. The y-coordinate of V is 3 and the y-coordinate of V prime is 7, so the point moved up by 4 units.
Now, let's examine each statement:
A. **The point moves two units left and four units up.**
**False.** The point does not move left; it moves vertically up only.
B. **The transformation rule is (x, y) right-arrow (x + 0, y + 4).**
**True.** This rule indicates no horizontal movement (x + 0) and an upward movement of 4 units (y + 4).
C. **The transformation is a vertical translation.**
**True.** The point is translated vertically since it only moves up.
D. **The image is four units to the left of the pre-image.**
**False.** The image is directly above the pre-image, with no horizontal movement.
E. **The translation can be described as (x, y) right-arrow (x minus 2, y + 7).**
**False.** The x-coordinate does not change (-2 remains -2), so the correct translation does not include changing x by subtracting 2. The correct transformation should involve adding 4 to y, not 7.
In summary, the true statements are:
- B
- C
1. The x-coordinate of V is -2 and the x-coordinate of V prime is also -2. This means the point did not move left or right horizontally.
2. The y-coordinate of V is 3 and the y-coordinate of V prime is 7, so the point moved up by 4 units.
Now, let's examine each statement:
A. **The point moves two units left and four units up.**
**False.** The point does not move left; it moves vertically up only.
B. **The transformation rule is (x, y) right-arrow (x + 0, y + 4).**
**True.** This rule indicates no horizontal movement (x + 0) and an upward movement of 4 units (y + 4).
C. **The transformation is a vertical translation.**
**True.** The point is translated vertically since it only moves up.
D. **The image is four units to the left of the pre-image.**
**False.** The image is directly above the pre-image, with no horizontal movement.
E. **The translation can be described as (x, y) right-arrow (x minus 2, y + 7).**
**False.** The x-coordinate does not change (-2 remains -2), so the correct translation does not include changing x by subtracting 2. The correct transformation should involve adding 4 to y, not 7.
In summary, the true statements are:
- B
- C